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Oh where to start...
I basically ship nothing canon on Buffy, Angel is a slightly different story. My main Buffy ship was Buffy/Giles, still is for that matter, but I also like Buffy/Xander, and Xander/Willow (semi-canon at least) before anything canon.
Harry/Hermione, now and always. Also like Neville/Ginny some Ron/Luna and movie-verse Harry/Luna.
I'm not sure I can name anything on Doctor Who or Torchwood that I ship which isn't canon to some extent. Doctor Who because most things kind of pale next to Doctor/Rose which IS TOTALLY CANON (and has been written that way from day 1 basically) and Torchwood because really what *isn't* intentionally played with in canon? However for a long time I shipped Jack/Tosh, toyed with the idea of Jack/Donna and still enjoy the possibility to Jack/Donna (not that I dislike Jack/Ianto)
While I OTP Mulder/Scully, I also like the idea of Scully/Skinner.
Guy/Marian (Robin Hood), okay that one isn't exactly ignored by canon, but I really liked it. Oh and Robin/Much and if the writer's aren't doing it intentionally they are at least doing it consistently.
Back when I watched Smallville I shipped Clark/Chloe and Clark/Lex (about even at first, more Chlark by the time I stopped).
I ship Sam on SG1 with basically everyone and I'm sure they aren't all intentional. Jack, Daniel, Janet, Martouf, Cam, and Jonas all spring to mind pretty quickly.
And let's not forget my self-invented Rose Tyler/Daniel Jackson pairing that I absolutely love even if it's just in my head. There's no way that was intended by anyone.
I'm probably forgetting some, I am a compulsive shipper after all, but a good portion of the time I go for the canon ships, and when I don't it's the ones I think should be canon.