In the TV show Stargate SG-1, how many missions through the stargate did the SG-1 team go on?
Depends. Is there conclusive evidence we were shown all missions? Perhaps they went on a lot of boring ones, which never were shown in an episode. Also what counts as mission? If they go on a mission to do x on planet y and they return saying, "x wasn't on y but we learned it's on planet z". Would going to z count as a new mission or as the same mission again?
Anyway, at some point they celebrate the 200th episode, coinciding In-Universe with Mitchell's 200th trip through the gate. He was introduced in episode 175 (Avalon). Which means 25 episodes mean roughly 200 trips. If we extrapolate from that, we get about 214*200/25 = 1712 trips in total. Seeing that they return to earth via the gate in most cases, gives an upper bound of about 850 missions.
I'd say at least every second episode they get a completely new mission (almost all missions involve the gate), so that would leave us with a lower bound of about 100.
I guess, if you want a more precise answer than between one and eight hundred, somebody will have to do the counting, re-watching every single episode.