The game that changed everything for me was Dogs in the Vineyard. I tried to play it safe, but our GM pushed me do act on what "I" believed in. Nothing was ever the same again. What I said was divine law, but I could not keep quiet.
This taught me two things. First was how emotionally charged and powerful a rpg session can be, and second how intense it can be when the players actions is what really matters, not what the GM has planned.
It was also something special to play religious nutjobs with a totally repulsive social baggage, and to both be very engaged and totally cut off from how such a weird person would think. A total mind job. Very much a mental upheaval.
Fate was the second game that it really threw me, this time as a GM. I could prep anything in five minutes! Having played D&D3 where the stats blocks are a bunch of math and unwieldy lists of feats, and then suddenly be able to use the Fate Fractal and just slap a few Aspects on anything was a revelation. That is how GM prep should be like! Sadly I have not been able to make the system really click in play, but it showed me prepping can be engaging and fun.