OTP ship: None. Really. I've been a Whofan since childhood; my love for this show is not based on shipping. Perhaps humanity/universe, or hope/universe, since that's the shows OTP.
Canon ship: I have a high bar for what I consider truly canon, and it's hard to think of pairings that qualify that I like. Delta/Billy, Brig/Doris, Bambera/Ancelyn (Battlefield is a world of shippy, both text and subtext), Mickey/Rose. And if I could see the subtext for Karra/Ace as a pre-teen, that ain't subtext anymore, that's canon. Maybe?
"If this happens I'll stab my eyes out with a spoon" ship: Explicit Doctor/Companion. Sorry.
"You are one sick bastard" ship: Not sure exactly what this is asking. If it's asking what ships squick me but I can still see -- One/Vicki. If it's asking what I ship that squicks others, then it's the ones that squick the all-about-the-pretty fans: Ten/Yana, Six/Evelyn, Doctor/Master on the Valiant with no deaging.
"I dabble a little" ship: Doctor/Jack. I only like it if it's set way post-series, where Jack is approaching or past the Doctor's age. Dunno why, just do.
"It's like a car crash" ship: In the "can't look away" sense: the Gwen/Rhys, Gwen/Owen triangle. In the "is going down in flames" sense: Doctor/Master, all incarnations.
"Tickles my fancy but not sold quite yet" ship: Two/Jamie. I like them, but I haven't found fic for them that doesn't hit my lingering Doctor/Companion squicks.
"Makes no canon sense but why the hell not" ship: I have this niggling plot bunny (but as I cannot write dialogue worth crap, it is just in my head) for Rose/Romana with Romana never having come back from E-space. I don't know why.
"Everyone else loves it but I just don't feel it" Doctor/Romana. I love Romana, especially Mary Tamm's version, but the pairing doesn't work for me. Perhaps it's just having been told before ever seeing the episodes that Tom Baker and Lalla Ward were falling in love during filming -- it all comes across as Tom/Lalla, and not Doctor/Romana, and hits my RPF squick head-on.
"When all is said and done" ship: Dunno if I have one. Going to have to go the cop-out route and say Doctor/TARDIS.
Finally, an addition, in honor of Martha Jones, who is awesome:
"Only when it's unrequited" ship: Some of my favorite ships I only like unrequited (Doctor -> Brigadier, Doctor -> Ace). And I really like unrequited Rose -> Doctor, but not requited. I'm not actually that fond of the two canon ones (Jack & Martha). And Sarah Jane -> Doctor makes me sad.