This rant comes in the form of levels of canonicity. Without further ado:
Dan/Tsunade: Yes. I am aware that there are probably JiraTsu fans out there who bash Dan, which kind of strikes me as pointless. He may have been a plot device, but by that token, you could call Yondaime a plot device, too. Sometimes you need plot devices.
Hayate/Yuugao: Also yes. I don't expect people who fell in love with a Hayate slash pairing prior to this couple's revelation to suddenly abandon ship, but at least acknowledge that this one is canon. Also, is this not the cutest ever?
Fugaku/Mikoto: They were probably cousins. It would explain Itachi and Sasuke so well.
Yoshino/Shikaku: Fawn abuse is mandatory.
Implicitly Canon (Or Going To Be)
This is where I expect to piss off the most people. Let's get started!
Sasuke/Sakura: For a while, this could have gone either way. For a while, I actually started to suspect that even though I preferred SasuSaku for the angst, she'd wind up with Lee for a Happy Ending. Not anymore. The timeskip gave her plenty of opportunity to give up on Sasuke--and instead she became a great ninja for his sake. This kind of obsession isn't exactly healthy for her, but it's clearly canon at this point. She chose Sasuke. She had the opportunity to choose Lee or Naruto, but she didn't, and now she can't go back. It's entirely possible Lee has gotten over her at this point, and in their analysis of the SasuSaku pairing, zauberer_sirin points out that Naruto's relationship with her has changed. He's accepted that she loves Sasuke, not him, and hopefully, Kishimoto will stick to that--but that'll go into my NaruSaku rant.
Now, there's still the issue of whether Sasuke can ever love her back. He's broken as hell, so this is a good question. It's true that she's important to him. I'm not sure Kishimoto has done the best job of illustrating this just yet; he's focused more on how Naruto is important to Sasuke. But there have been moments. If Naruto represents his goodness and light, Sakura represents his simple humanity. This is best shown in the Forest of Death, when she embraces him while he's raging and inhuman, and he slowly returns to himself.
And then, of course, there's chapter 181. This is not evidence that he doesn't love Sakura and just wants to brush her off. It's evidence that he's so fundamentally broken that the only way he knows of to express his feelings for her (which aren't actually love at this point, because he doesn't know how to love) is to smile when he says she's annoying, thank her, and then put her to sleep so that she doesn't get herself hurt by his own darkness.
No, I don't think he's madly in love with her and hiding it out of pride. That's just stupid. However, if he'll ever be able to love anybody, it's her. Likewise, there's nobody else she'll be willing to settle for at this point, even though this is rather tragic for her, as she could have had a pleasant normal love life with some other boy. On the other hand, if she'd gone for that, she'd never have blossomed into the superb ninja and strong young woman she is now. Her love for Sasuke makes her life complicated and more than a little sad, but it also pushes her to heights she would never have otherwise even considered. The front she presents to the world might have been happy with Lee, but Inner Sakura needs someone troubled and demanding like Sasuke.
I'm not yet sure whether these two will end up happy, mind you. They could wind up in tragedy instead. I don't think that's the way it'll go, though. At this point, the only thing that makes me hesitate is the possibility that Kishimoto will cop out and toss Sakura with Naruto, but I'll get to that later.
Naruto/Hinata: It's certainly there. Hinata is very obviously all over him, and Naruto, for all that he's too dense to actually notice how she feels, has told her that he likes people like her. So that much, at least, is canon. It doesn't hurt that they're just what they need in each other. Hinata is all love and acceptance for Naruto, and he brings out the strength in her (the dynamic has echoes of the SasuSaku one, it's just a hell of a lot fluffier).
The only question, at this point, is whether Kishimoto's going to bother, or if he's decided that Hinata is too minor a character to pair with the hero. Me, I'm still holding out hope that she'll show up again soon. People who want to dismiss her so readily seem to forget that she showed up again, and in the context of her feelings for Naruto, right before the timeskip--and it hasn't really been that long since then. I'm still hoping Kishimoto's going to get to her again.
Temari/Shikamaru: This strikes me as the only pairing among the non-primary characters to have enough evidence so far to cement it as implicitly canon. And before you start bitching me out, no, I'm not talking about the fight. I didn't see any evidence for these two in the chuunin exams. But the later stuff? You don't do that to a male and female character in a shounen comic unless you at least want to imply that there's something potentially going on there. Shikamaru makes reference to a "scary yet beautiful" smile. That in and of itself is also hardly evidence, but...there is no other character that he so much as bats an eye at, romantically. Seen through the perspective of their exchanges then and later, just before the timeskip, the rest of their relationship does have a distinct romantic edge to it.
I'm not baffled by the people who don't think these two suit each other for a long-term relationship. That's a matter of opinion. Hell, even I think they're more intended for an off-and-on sort of thing, and they're my OTP. What floors me are the people who don't see any canon basis at all.
But hey, since this is my journal, I'll go into more detail. To me it's a matter of want versus need. What Shikamaru wants is a nice peaceful life where he spends his days watching clouds and playing shougi. What he needs, to bring out the potential within him (and this seems to be a running theme in Naruto's relationships), is someone he doesn't quite understand, someone who will keep him on his toes, someone foreign and strange. Temari.
As for why she wants and needs him...well, who wouldn't?
It's just a matter of whether or not Kishimoto ever gets around to giving us more information.
Neji/Tenten: The only girl Neji's paid more attention to is Hinata, and that was not in a romantic context. Certainly Tenten seems to pay a lot of attention to him--although that could just be as a matter of narrative device. The hindrance here is that poor Tenten has never gotten much personality or screentime. I am very much hoping she gets a chance to shine in the upcoming chapters, and that maybe we get to see more of her relationship with Neji, but I'm not holding my breath.
Ino/Chouji: I don't have the manga on hand to check, but I'm pretty sure Ino has more interaction, or at least on-screen conversation, with Chouji than with any other male character. She also pays more attention to him than to any other boy besides Sasuke. She even makes reference to him looking good when he first got out of the hospital, just prior to the timeskip. That's not much to base a pairing on, but it is more than she's ever said about anyone else other than Sasuke.
On a deeper level, it's more about irony and reversal of expectations, as Team 10 in general is. Ino is the pretty girl, the popular one, with a shallow crush on the prettiest boy in town. Chouji is the outcast fat kid who also happens to be very sweet and kind. Nobody (except, perhaps, first-gen InoShikaChou) would expect the two of them to wind up together, but Chouji would be more there for Ino than any popular prettyboy.
As it stands, though, we just don't know enough to reach a firm conclusion. Hopefully, Kishimoto will bring these two back enough to give us more glimpses of them together, because they are painfully adorable as a couple.
Jiraiya/Tsunade: We know that Jiraiya once had a crush on Tsunade. We know that these days, they're all that's left of their team that hasn't gone evil. They're there for each other in ways that nobody else can be. We don't know if Jiraiya still harbors those old feelings for her, or if they're gone for good. Whether Tsunade could ever reciprocate is also completely up in the air. I love these two together, but canonically, the information to prove or disprove anything isn't there yet. Personally, I doubt it ever will be.
Asuma/Kurenai: They are together a lot, aren't they? I seem to recall that when they crop up outside of teaching their teams, it's together. I also think I may be forgetting something else, but oh well. In any case, this is another one that would certainly make sense if we were given more information to prove it, but as it is, it's impossible to draw any sure conclusions.
Kakashi/Rin: It's pretty obvious that Rin at the very least had a crush on him. What's left up to the imagination so far is whether he ever figured it out and reciprocated. Let's face it: tiny Kakashi was an emotional moron. He still has trouble actually relating to people, but nowadays he can at least understand them. It is not that much of a stretch to assume he stole that part of himself from Rin. But how did he actually feel about her?
My theory is that he loved her, but he didn't realize it until she was dead or close to it. It would fit with the general too-little-too-late brokenness of Team Yondaime, and it seems to make sense in the context of Kakashi's character. It is, however, possible that he managed to open up to her for a while before her death. We simply don't know for sure.
And yes, it's technically possible that she's not actually dead, but at the very least, Kakashi has to believe she is. He outright says so to Sasuke: the ones he loved most have already been killed. I don't think he would have lied in that situation.
Not Canon, But Not Implausible
These are the ones that could have been canon, but never accumulated any evidence to support them, and don't seem like they will in the future.
Kiba/Hinata: I admit I've never seen any evidence for these two. I never read Kiba's affection for her as anything but a typically canine loyalty and protectiveness. However, they are teammates, and they surely care about each other. Assuming Hinata's obvious feelings for Naruto can be dealt with, this pairing is feasible if not actually canon.
Shino/Hinata: Pretty much the same as the above, only without the big fandom, because Shino is bug boy and therefore unattractive to the fandom at large.
Shikamaru/Ino: My kneejerk reaction to this is always 'why?' But to be fair, I know why. Same principle as the above two: they're teammates, which makes Ino the closest female to Shikamaru (and for the shallow fans, Shikamaru is the hot one and oh my how could you ever think of pairing Ino with Chouji, he's fat! Ewww!). Neither has ever once expressed attraction or potential attraction for the other, but it's not an entirely unreasonable idea that they could wind up with each other. Ino is, after all, the girl next door, and Shikamaru would by default wind up marrying the girl next door if he didn't get nudged onto another track.
Neji/Hinata: I hate this. Hate it, hate it, hate it. My God, they're genetically half-siblings! And neither of them has even once indicated that they think of the other as anything but a family member. Well, and someone to kill, in Neji's case, but the boy was messed up, so moving on! The fact is, Japan has no taboo against cousin incest, and Hinata is the most important female in his age group to Neji. Plus, they do have plenty of opportunity to interact.
Tenten/Lee: This is about the only Lee pairing I can tolerate, and even then, the thought of going beyond mild romantic overtures breaks my brain. There's even less actual evidence for this than there is for NejiTen. But yes, teammates. And I suspect Tenten is the only girl who can put up with Lee.
Into this category also go such pairings of minor characters as Genma/Raidou and Kotetsu/Izumo. We rarely see them apart from each other, but then, we rarely see them at all. So it's certainly possible, but we're not likely to ever find out enough to say for sure.
Could Have Been Canon. Now They're Not
Sakura/Lee: Yes, I know. You love Lee and you want to dance on Sasuke's grave. Or maybe you just want to dance on Sasuke's grave and shove Sakura into the nearest fluffy relationship. (Generic "you" used here. I doubt people reading this actually feel this way, but I've known too many people who do.) In either case...at one point, this could have happened. Sakura could have chosen to give up on Sasuke and settle down with Lee...but by now, it's very clear that she didn't and she won't.
This is probably a good thing. In retrospect, it makes the most sense if Lee had never really intended (at least on a subconscious level) to wind up happy and domestic with Sakura. He sets impossible goals for himself; that's how he becomes strong. Sakura was the ultimate impossible goal. The point wasn't to actually get her; it was to encourage himself to grow. He succeeded in making her respect him, and that's pretty impressive given how shallow she was, and how dorky he was, when they first met. But I suspect that ultimately, on some level he never really thought of her as a love interest.
Why, God, Why?
Kakashi/Iruka: I'm not surprised to see these two slashed. It's a popular shounen series. Everyone gets slashed. What will hurt my brain forever is the inexplicable enormity of the fandom for this couple. It is probably the second-most popular pairing in the entire fandom. Why? Dear Lord, why?
Kabuto/Temari: No, seriously, what the hell?
I--at this point I'm going to stop listing pairings and start listing categories. Note that I'm not talking about the people who write occasional one-shots or smut about an unlikely pairing (I have no intention of stopping that any time soon myself, at least not before I get the Tsunade/Anko request for sadieko finished), but the ones who cling to it as an OTP against all logic and reason.
Characters Who Have Never Met In Canon: Sure, it might be hot. But, uh. You do realize that they've never met? Seriously.
Characters Who Fought Once And Had No Other Significant Interaction: Stand still so I can punch you for making the TemaShika fandom look bad.
Mentor/Student: Okay, so Zabuza and Haku might have had a certain doomed romantic element to their feelings for each other. I'm not ruling that out. But that's about the only one that I can think of with any possible canon support. The rest? Most of them just creep me out.
Kakashi/Anyone Still Alive: It is a fundamental part of Kakashi's character that he is too profoundly lonely to be fixed by some new person waltzing into his life. So quit it with the fluff, okay? Especially the KakaSaku. It hurts. Properly done, it's a brief moment of angst; improperly done, it's a desecration of both their characters.
Gaara/Random Person: Have you ever tried having sex on a beach? Getting sand in very personal places isn't as fun as it sounds. And it doesn't sound very fun.
Not Canon, But...
Naruto/Sasuke: Look, it's a shounen series. The two main male characters are not going to wind up romantically involved, not in canon. And you can't base your argument for a pairing being canon on a single accidental kiss from near the beginning of a series. That said, though, I think it's a more reasonable pairing than most of your standard Pair Up The Protagonists, Quick! yaoi couples. It's certainly closer to canon than most; they do have that kiss, and they're very important to each other. My usual problem with Random Yaoi is that it takes a perfectly well-defined relationship and makes it all about sex in ways it never was in canon, but the whole thing that makes Naruto and Sasuke's relationship so interesting is how poorly-defined it is. Neither of them really understands how to interact socially, so their relationship oscillates among rivalry and friendship and brotherhood and everywhere in between. I think the kiss mostly exists to presage how strong and important their relationship would become--but the messiness of it makes it pretty easy to slash them in certain situations. Of course, sappy romance and hot, hot twelve-year-old sex...are not among those situations. But comedic NaruSasu, violent NaruSasu, awkward crazy NaruSasu--so long as it's well-written, I can see it. But canon? No. I do, however, think that it has more canon backing than, say, Roy/Ed or Ishida/Ichigo. Which, granted, isn't saying all that much.
Naruto/Sakura: ...ngh. I suppose my reaction to this is partly an irrational aversion, but I just can't see it. Naruto loves her, but it's become clear that he's accepted she doesn't love him romantically, and his own love for her seems more sibling-like than anything else at this point. It's been pointed out that he's accepted she's not going to stop loving Sasuke; he promised to bring Sasuke back for her without any regret or whining, and even though he failed, that doesn't change the fact that he tried his hardest. For a while, their relationship has struck me as extraordinarily sibling-like, to the point where romance between them would seem nearly incestuous. He hasn't made any attempt to hit on her since the timeskip. In short, the pairing seems pretty much dead.
On the other hand, it's also been pointed out that in shounen series, the hero always has to wind up with the girl he wants from the start. So if Hinata continues to be absent, well...NaruSaku looks more and more likely. I'm still crossing my fingers that Kishimoto will let actual characterization hold more sway in the series than shounen convention, though, since characterization has always been its strong point. On top of that, there's the fact that Sasuke is his favorite character, so it's not out of the question that he, as the anti-hero, might wind up with Sakura instead. But the usual standards of the genre mean that for now, this pairing goes here instead of in the 'Could Have Been Canon. Now It's Not' section.