chimera201 :
1. DiRT 2
2. GRID
3. Need for Speed: Most Wanted 2005
4. Burnout Paradise: The Ultimate Box
5. Need for Speed: Hot Pursuit 2010
6. DiRT 3
Besides these, DiRT 1, if you can get it, is very good. Also NFS Shift 1&2 are pretty good. I also liked NFS Rivals, and even NFS The Run has some good stuff in it, though a bit short, buggy, and contrived with the mob element.
I've also played GRID 2 and GRID Autosport. GRID 2 has some nice narrow tracks that GRID 1 didn't, but overall not as good a game. Sadly the multi view replay cam is woefully inadequate and cockpit view non existent. Autosport brought back lots of circuit tracks, but plays horribly on KB, you really need a pad or wheel. It also brought back cockpit view but it's horribly implemented, and the vehicle tuning and damage model in both GRID 2 and Autosport are nothing compared to GRID 1.
The race game that may be the best one ever made is releasing in Nov, called Project C.A.R.S. You'll probably want a pad or wheel for that though. I have however seen a nice video showing someone putting in a pretty decent lap at Nürburgring on KB in a build version some time ago, and KB response was one of the last things they were working on, so it's only going to get better.
[video="https://www.youtube.com/watch?v=D8MZ64QWfIs"][/video]
[video="https://www.youtube.com/watch?v=lgCPypsg5vU"][/video]
Latter build (6/14) on keyboard
[video="https://www.youtube.com/watch?v=SQMr_-LNbAo"][/video]
Older build (2/13)
[video="https://www.youtube.com/watch?v=T4Yp7gpL4Wc"][/video]
If you want to expand into regular (mostly shooter type) games that have lots of driving, you may want to also check out GTA IV and V, and Sleeping Dogs and Watch Dogs. Sleeping Dogs is more of a martial arts/shooter though.