Forza 2 great. Like the Xbox GT equivalent. Find the bonnet view not too bad
Have a 700bhp Volvo, a Saab with a RWD conversion and a tasty Delta
Flatout is fun in a destruction derby kind of way.
The Project Gotham games are quite good but focus on high end sports cars. Have 3 and 4 on 360 / 2 for Xbox1, 1 I have in the Dreamcast incarnation MSR.
Nascar 2009 - I used to love the old Papyrus Nascar games on the PC in the late 90s, but this I found too fiddly, forever having to correct the steering. I know that they have pronounced wheel stagger to allow for turning left on ovals, but it gets a bit annoying. Perhaps would work better with a wheel.
Dirt is good, part of the codemasters Colin McRae rally series.
I have Sega Rally which is slightly less arcadey than the Dreamcast version, but still fun for an hour or two.
If you liked the Toca codemasters series, Race Driver Grid was ok on the demo.
Burnout Paradise you need the reactions of a fighter pilot to have any chance of success with!
Enjoyed Burnout 3, which can be downloaded from arcade. The crash mode with the x4s and explosion tokens were a great 'puzzle' to try and get consistent gold
GTA4 isn't really a driving game, but in HD looks stunning, like a pseudo-realistic New York. Saints Row is similar, but has no in-car view, and the camera takes an absolute age to follow you round corners
As an aside, I was having some old school fun on the dreamcast and found this amongst my collection, chuffed to see the GTV on the cover
http://www.jonscanlon.com/ebay/vanishing.jpg