Can't really say what would be the ultimate best moment ever, but I just remembered these reading the thread title.
Best racing sim moment(s):
My first real race ever in a "real" sim (it was NR2003, in Watkins Glen I think).
Before the lights went off I was really nervous like I would be IRL when doing first race start ever.
First race win online in S2.
Best FPS moment:
The old-good BF42, with Forgotten Hope mod and some addon map to it, I was playing on allied and we had a bad situation, we were hiding behind some bushes and trying to think about good way of getting over the big open area with constant axis mortar bombing. We chatted and thought like maybe it's just best that we all rush at same time, teh nazis can't get us all rite? So we all shouted charge thru the radio and run over the open area with mortar grenades blowing off, most of us died but I and few team members got to the enemies trenches and killed them in close battle, I was using my favorite weapon M1 garand.
Now the way to the village was open, it was the best moment but it was only start of the battle, trying to get the village was very thrilling too.
Can't remember the maps name but it's maybe the most awesome FPS multiplay map I've ever played.