Most of these have more than one pairing. Because the cast of Bleach is huge. ^_^;

One True Pairing Ship: Yoruichi/Soifon probably qualifies most for this one.
Canon Ship: ...Yoruichi/Soifon again? Or Ikkaku/Yumichika. Those are both totally canon. >_> ... okay, if I'm picking an actually explicitly stated ship, Orihime->Ichigo, because I wasn't shipping them at all and her goodbye nevertheless made me woob and cry a little.
"If this happens I'll stab my eyes out with a spork" Ship: Um. Er. Oh! Nel/Nnoitra - I acknowledge that they have an interesting relationship, but all I want to see her do with him is kick his ass into next week.
"You are one sick bastard" Ship: Szayel Aporro/Ishida/Renji.
"I dabble a little" Ship: Tatsuki/Orihime. Also many others, to lesser degrees.
"It's like a car crash" Ship: Ulquiorra/Orihime.
"Tickles my fancy but not sold just yet" Ship: Man, there are a lot of these. Grimmjow/Orihime, Grimmjow/Ichigo, and Ichigo/Orihime all. Isshin/Ryuuken. Aizen/anyone. Others, I'm sure.
"Makes no canon sense but why the Hell not" Ship: Ishida/Renji? They have banter and stuff, though. I'm sure I can be more WTFish. Probably Kuukaku/Tatsuki. It makes sense in my head.
"Everyone else loves it but I just don't feel it" Ship: Anything with Byakuya. Probably Byakuya/Renji's the most popular of those. Also, Urahara/Yoruichi.
"When all is said and done" Ship: Not sure. Shunsui/Ukitake, maybe. They have clearly been together for more than a century. Or Ishida/Ichigo, which was my first Bleach pairing.