There aren't many of these in Bleach. It's about family, not romance. That said, they are there; Kubotite is just very subtle about them.
Byakuya/Hisana: It happened. And she died. And now Byakuya is asexual. At least, I hope so.
Isshin/Masaki: I really hope Isshin is asexual now. At least, unless Masaki turns out to be not dead or something LIKE HER SECRET TWIN BROTHER. come on you know ICHIGO I AM YOUR UNCLE would be so hot
Kaien/His Wife: I'm sure when we find out what her name is, it'll have Deep Symbolic Implications. Either that, or we'll never find out because the series will never mention Kaien again.
Chizuru/Orihime: This is the best thing ever. God bless KT and his lesbian fetish.
Hinamori/Aizen: She is so sad and so cute. Doesn't she even comment about loving his smell? Poor girl is so smitten.
Rukia/Kaien: Oh, the angst.
Everyone/Hinamori: Because Soul Society is all about the loli.
Implicitly Canon (Or Going to Be)
Rukia/Renji: I have no interest in this pairing. They seem so platonic to me. But it is rather strongly implied as canon, insofar as KT goes. I just don't really care for the way he writes romance.
Ichigo/Orihime: This is Pretty Damn Obvious. There's a strange and rather strong--almost psychic--bond between the two of them, right down to their hair. It's a Fated sort of thing. Personally, I do not find it romantic at all. Even from Orihime's side, her understanding of "romance" is strange enough that I don't think her obsession with Ichigo has to be romantic in nature. But like I said, I don't think I'm on the same page as Kubotite when it comes to romance. This causes me endless agony, since normally I'm a total canon whore in regards to pairings. I was so spoiled by Naruto, where I am all about the implied canon pairings. :(
Shunsui/Nanao: Okay, this one I can see. In fact, to me, it's the most obvious of the implied canon pairings. Why else would she put up with him? Come on.
Rangiku/Gin: This one is almost reciprocated. Almost. Gin certainly has more history with her than with anyone else (except possibly Aizen), and the way he treats her is different than the way he treats everyone else. But even with her, he's taunting and distant. My take on it is that she's his favorite toy--but since this is me talking, I'll grant there's a possibility of it being more than just one-sided someday.
Hanatarou/Rukia: This could just be me and my not-so-secret RukiHana fetish, but he seems kind of infatuated with her. Romantic or not, it's adorable.
Ishida/Orihime: He acts endearingly like a smitten teenager around her. However, it's possible that this is just the way anyone as uptight as Ishida would act around someone like Orihime, so it could be nothing.
Hitsugaya/Hinamori: You know, I don't think Hitsugaya's actually admitted to himself that he feels that way about Hinamori. Captain Shota is so adorably dense. I'd almost label this as one-sided, except...I think it's possible that someday Hinamori will return his feelings. She does care about him, or she wouldn't have been so upset about her orders to skewer him; she says as much. Plus, as far as Soul Society goes, KT has proven that he's fond of childhood-friendship pairings.
Yoruichi/Soi Fong: I don't see Yoruichi having romantic feelings for Soi Fong, but given my track record with other pairings in this series, I'm not about to call that canon. I can, however, buy that she would develop them. As for Soi Fong's feelings for Yoruichi? I am always hesitant to call canon on gay pairings, but KT loves his lesbians, and it's pretty obvious that Soi Fong is all about the Yoruichi. So that much is obviously canon.
Ikkaku/Yumichika: Peacock boy is obviously gay. So very gay. And he does have some interesting interaction with Ikkaku. However, I'd say we still haven't seen enough of them to call it implied canon for sure.
Karin/Chad: The way they interact is very interesting. There's something wonderful about how their characters mesh: Karin as tiny but fierce, Chad as huge but gentle. However, since I love this pairing, I'm very unsure about its potential for canonicity.
Ichigo/Rukia: Kubotite hates this pairing. He mocks it throughout the time they're together. Neither of the two of them ever indicate any romantic affection for the other. This is, naturally, my greatest shame in all my Bleach obsession. I hate the fandom tendency to instantly pair Major Male Character A with Major Female Character B--this is where Ed/Winry (which, admittedly, I don't hate, but I don't obsess over it the way half the fandom seems to), Naruto/Sakura (please please please Kishimoto don't make this canon), Spike/Faye, and the majority of pointless het pairings in general come from. And yet I love IchiRuki. Why, God, why? Why must my own fickle inner fangirl betray me like this? WRRYYYYYYYYYY
Urahara/Yoruichi: Since I love these two, we can assume that they're not canon. Also, there's just plain no evidence for them aside from the fact that Yoruichi radiates sex wherever she goes in human form, and the fact that she gave up a high-ranking, privileged life just to follow him into exile--sorry sorry that's my inner YoruKisu fangirl speaking again. D: Anyway, it's not as blatantly !canon as IchiRuki, but there's been no evidence for it yet.
Tatsuki/Orihime: BUT I WISH IT WAS
And now for the fun part.
Ichigo: Mostly asexual at the moment; eventually straight. (He certainly reacts more to half-naked or naked women than to half-naked men. Even if it's not precisely a positive reaction.) Usually a top, on rare instances a switch.
Isshin: DON'T MAKE ME THINK ABOUT THIS
Rukia: Straight. Top. For all her insecurity and self-esteem issues, the people she forms the most permanent and potentially romantic relationships with are ones she's likely to dominate on some level. She's submissive in some of her relationships, true--most notably with Byakuya--but these are the least romantic ones. (With the exception of Kaien, but that was some time ago, and it never developed into anything, since he was married.)
Orihime: More or less straight eventually. For all her feelings for Ichigo, she doesn't seem to think much about actual sex. As for the "more or less" part, well, KT loves his lesbians, so there's always the possibility. I'd label her as a bottom most of the time, but not completely averse to topping.
Ishida: Probably straight (he acts like an uptight but straight boy around Orihime, certainly), but given how fruity he is, it's hard to say for sure. Switch, because he'd totally try to top Ichigo (I don't know if he'd succeed), but he'd go instantly submissive for Orihime.
Renji: Straight, tops everyone but Rukia (at least on an emotional level).
Byakuya: Mostly Hisanasexual, probably mostly a top.
Kenpachi: Asexual, would FIGHT to top anyone.
Yachiru: Asexual until she grows up; who knows what then?
Yumichika: Gay, gay, gay. Will bottom for anything pretty with a penis.
Hitsugaya: Straight, would gladly bottom for Hinamori but probably winds up topping usually.
Rangiku: Straight, switch.
Hinamori: Straight, wants to bottom but could top half the men in Soul Society if she only realized it.
Aizen: Asexual, because everyone is as a child to him. Tops everyone.
Gin: More or less asexual--he's too sociopathic to relate to people well--but what little romance there is in his soul is of the straight variety. Would top everybody but Aizen.
Ukitake: Probably straight, but since it's not stated in canon we can't actually be sure. The sort of guy who tops from the bottom.
Izuru: Straight (although he'd gladly do Gin if he were asked), so very bottom.
Urahara: It's hard to say. I mean, I want him to be at least bi, but my abilities to detect this sort of thing for this series are dubious at best. For now, I'll say bi, because he's just too flaming to be completely straight, but he doesn't seem entirely gay to me either. I think he's mostly Sciencesexual: attracted to whoever is the most interesting. That doesn't mean he'd always act on it, though. For instance, I can buy him being attracted to Ichigo, but not acting on it, since he wouldn't mess up an Experiment by getting involved with them. Also a switch. He'll be whatever makes things more interesting.
Yoruichi: Bi, top. Probably gets kinky without even realizing it.
Soi Fong: Gay or bi, could top but probably wants to be dominated. :D
Mayuri: Even more Sciencesexual than Urahara, but less gay, since he shows clear preference for women. Top; more of a Just Plain Sadist than anything else.
Nemu: Straight, was made to bottom.
Shunsui: Straight, probably a switch (he'll be whatever his Nanao-chan wants).
Nanao: Straight, top.
Maybe I'll list some more later.