Def Mulder and Scully, for all the reasons you mentioned, as well as the fact that they complemented each other so well. Also, they're pretty. It's hard to say when it started, because I didn't start watching until S4 or so and then proceeded to watch it out of order. (I still haven't seen every episode. Blasphemy!)

Sara and Grissom on CSI were probably my only other significant ship, in terms of participating in the fan community and reading fanfic and whatnot. I liked them because they were both very similar people (smart, reserved, obsessed with work) who brought out unexpected qualities in each other, and, just like Mulder and Scully, their relationship was subtle, gradual, and only had a payoff a few times a season. :)

I'm also a Roslin/Adama shipper, but I never really did anything about it beyond squealing and flailing like a little girl.