NFS5: Porsche Unleashed is one of the most realistic games around. The physics of the game are a lot more realistic than most other games. It is an older game, the graphics look dated, and it isn't as detailed as I'd like but, the way the cars handle is all worth it. The handling physics of each Porsche in this game are similar to the real thing. RWD 911's (especially older torsion bar ones) are rear heavy of course, and the handling reflects this in the game. Though, if you know what you are doing, 911's can be extremely potent drifting machines!

This games only about $5-15 and well worth the money IMO. Not the best but, it's still fun.
What's funny to me is that one of the best games in recent years isn't even a game! The GTR 2002 mod for EA's F1 2002 is one of the most realistic games available for PC. Though, when it comes to sounds, I won't hesitate to say that the GTR mod has the absolute best engine sounds out of any PC/console game in existance! They are as realistic as it gets. There are a ton of options to mess with as well, and there is even telemetry in game that you can use to help you tune your car!
LFS is pretty cool. The handling physics are very realistic and I like almost everything else about the game. I just wish they could include more cars, that you don't have to earn by racing and winning money. These guys have done an excellent job with this game, though. This is much higher quality than the offerings of many much larger developers like EA.