I usually stick to canon. The only relationship I'd actually watch (not saying that I would fan girl or whatever... Hopefully you get the idea that I don't really ship anything unless it is canon, and sometimes not even then) would have have to be Amy and the Doctor.
Lololololololol. That sounded confusing and weird and I'm probably making a fool of myself and maybe no one agrees with me.
I stick to canon for the most part. In fanfiction, I'm a huge Drarry and Dramione shipper, though.
I would have shipped Amy and the Doctor in early series five but now I just want Rory to have his happy ending. Plus I've become an avid Doctor/River shipper.