I certainly remember R: Racing Evolution. Just recently I pulled out my Gamecube and played it again. The Gamecube is pretty much why I own the game -- I didn't have a PS2 at the time and Nintendo systems have been devoid of (third-party, real-world) racing titles since the N64. The one thing that kept me from really enjoying that game was the broken countersteer. The physics aren't bad, but you can't recover from any significant oversteer angle.
Two underdog racing games I really really like are Enthusia Professional Racing (PS2) and FUEL (360, PC, PS3?). Anyone who knows me from GTPlanet is familiar with my affinity for EPR. Best physics realism of any console game for years, challenged only by FM4, in my humble opinion. And though FM4 has loads of details and a better tire model, I still think EPR has a better grasp on kinetics, the basic laws of physics. The car list is overflowing with what you might call "soul" and "character," the track list is mostly fictional but benefits from the creative freedom, the racing music -- in classic videogame fashion -- was written for the game and themed to each racecourse...this game is so charming and unique, I'll be playing it on an emulator years after the PS2 becomes a collector's item.
While EPR offers replay value by means of quality, FUEL offers replay value essentially through brute force. The map -- recognized by Guinness B.o.W.R. as the largest continuous game world...in the world -- is a mammoth of highways, back roads, mountain roads, gravel roads, 4x4 trails, and quad/bike trails, snaking over just about any sort of environment you could ask for...as long as it's not urban. The map is exceedingly rural, but that benefits the gameplay. The roads are rough and the world is devoid of people, but the storyline of "oh no it's a global warming disaster, now go race" explains away the ragged edges of the auto-generated terrain. The physics are vague, but surprisingly deep for an arcade game. There's not much to do, but you'll never run out of roads. It's a fundamentally but brilliantly flawed game, and a perfect example for this thread.