If you like fun racers, try Crash Bandicoot Nitro Kart 2. The online mode works very well, I spent lots of hours there and still play it every now and then, because there are always people online.
GT Racing: Motor Academy is the only real racing sim. Real Racing is very good, if you don't mind the lack of realism (it doesn't have very realistic physics). In my opinion, the best arcade racing games are Asphalt 6 and NFS: Hot Pursuit.