OTP ship: Ian/Barbara. Not that I ever fic it or anything. But they're both awesome individually and together they are just exponentially awesome. And their humanising influence is entirely responsible for the Doctor becoming a proper Good Guy. I got a lovely Ian/Babs fic for the otp_indomitable ficathon from bulky_monster. (Runner up in this category: Nyssa/Tegan)
Canon ship: Doctor/Master. Especially after the end of S3, but it's always been there. (Runners up: Ian/Barbara, Fitz/Trix)
"If this happens I'll stab my eyes out with a fork" ship: This category kind of has to be a current one, doesn't it? Or if old-school at least one that might happen in Big Finish. Non-year-that-never-was Martha/Tom. It's so horribly pasted-on to try and make that Martha's departure better. Yes, I'm still bitter. They had better do her Torchwood and S4 appearances right. Having said all which, I can see potential in Martha/Tom as a silly angst thing where he's all "Wait? You mean you've already met me and I died?" (Runner up: canon Doctor/Rose reunion)
"You are one sick bastard" ship: My kinky/borderline abusive take on Doctor/TARDIS.
"I dabble a little" ship: Mickey/Jake. Because Mickey is great and deserves it. (Runners up: every ship ever, pretty much.)
"It's like a car crash" ship: post-Time-War Doctor/Romana. Entirely a creation of fandom, but who cares?
"Makes no canon sense but why the hell not" ship: This is a bad category for me, I always always always try to have some sort of plausibility going on in the background. Luckily with near-omnipotent time travellers in the 'verse this is quite easy to achieve. So I'm just going to say something silly like Barbara/Lexa.
"Everyone else loves it but I just don't feel it" 'Ship: I'm going to have to say Doctor/Rose here, aren't I? The crucial member of "everyone else" is of course RTD.
"When all is said and done" 'Ship: Hmm, I would say Seven/Ace except I don't ship them because (my inner ten year old insists) that would be Wrong. Oh, OK, I'll be honest: it's Ten/Martha, because it's the first time I ever found myself invested in what would happen to a Who ship rather than just enjoying it as a bit of a fun.
ETA: Help! What's that comm with the long-form Who fic ficathon? If the deadline is nice and far away I might sign up for it to kick my three-years-in-the-making Turlough kink thing into gear.