I tend to dislike pure racing games so Carmageddon (3D) and Turbo (top down) were my favorite.

But I spent a lot of time on Stunt Car Racer.

Test Drive Unlimited.

Arcade: NFS 3 (High Stakes was great too, but still liked 3rd better somehow :S)
Sim: Live for Speed (didn't try rFactor 2 so far)

There was few other that I rly liked back in the days, like Toca 2, NFS Porshe/U2, or Viper Racing (ah that painting and damage, that one should be here on gog ^^)

Test Drive Unlimited
Forza 2

I don't really like racing games but sometimes if they have the right kind of fun arcade feel I can get into one. Burnout Paradise is probably the one I had the most fun with, unless you count stuff like F-Zero when I was a kid.

Personally, I had the most fun with Initial D Arcade Stage Version 2. I really enjoy the drift racing.

GRID
There are others. Of course there are others. But for me GRID just strikes absolutely the right balance.

I always liked Need for Speed III: Hot Pursuit. Something about outrunning cops in a Lambo or Ferrari.

I'm sure some here will remember Midtown Madness 2. Absolutely awesome and incredibly fun open-city racer!

It comes and goes based on release, as I usually only play current titles. Right now Gran Turismo 5 has all my attention, though I'm beginning to wonder if people are cheating online again.

Wipeout Pure on the PSP. It's the only one I tried to play in a more "serious" fashion, anyway. Still waiting to have the will to start my portable console again (in years) and complete my medals roster.

P.S.Oh, now I remember: there is Powerdrome running on my rusty 286 some decades ago, too :-P

And that's why I quit playing online. You could never tell if someone was cheating or not. I still do not understand why people cheat. For me it would be incredibly boring to cheat. I never even liked doing those Up+down+down commands on the early Nintendos.

My favorite would probably be at the moment sonic all stars transformed.

Need For Speed: Underground 2