I play a bit of racing games. I'm not that good at them, so I don't play every single one, haha. So aggravating to go through an entire race, then crash right at the end and lose.
But on suggestions, it really depends on what type of racing you're looking for and for what platform.
You've got your more traditional racing games, i.e. driving around some sort of circuit. On the 360, Forza 4 is apparently the best racing game there is. I tried 3 and thoroughly loved it, despite not being a huge racing fan. On PS3 you've got Gran Turismo 5, apparently a really really good racing game too. Stuff like Need for Speed: Shift 2, GRID and the F1 series are good too.
Then you've got Rally racing, basically off-road stuff, which the DiRT series absolutely nails. I played 2 when it came out and I loved it, and apparently the newest one, 3, is by far the best in the series.
Then you've got stuff like Need for Speed: Hot Pursuit, where much of the game is you out-running cops, racing other people, or playing as a cop trying to force some lunatic driver off the road. I haven't played much of the single player, but the mutliplayer is ridiculously fun.
Then we got other types of racing games. Blur is a typical racer, looks like one too, except for the Mario Kart type of power ups. Split Second has you playing as part of a tv-show, so it's a lot of over the top stuff like dropping building onto your opponents, lol. Burnout Paradise is supposed to be good too, a bit over the top with lots of crashes and stuff.