Trackmania is very good (the version you pay for) - loads of race types and the online play has had a huge amount of thought gone into it. The free one is quite limited on the track types, but give it a go to see if you like the online experience. Zero griefers, but can sometimes lack the excitement of other games.
GranTurismo 5 Prologue is fantastic, but limited by it being a prologue so there aren't many tracks. Plenty of online action but lots of grief players around so can be hard to find a good race. Not as great a leap in AI in single player as I expected either. The F1 simulation though is fantastic and is a real experience with a good wheel.
GTR2 and R-Factor are still around for the PC ultra-sim crowd. Personally as I have a life and don't want to spend 6 hours simulating practice / warm up / qually / 250 mile race and then have it all fall apart because I forgot to hit the pit lane limiter, but lots of people still love it
There's a free demo of the BMW M3 around Hockenheim for the PC somewhere based on the GTR2 engine I think - download that and see if you like the style.
I still haven't played GRID or the PGR series, so can't comment on them, though both have legions of fans