Midnight Club 3: DUB Edition Remix. I realize it's a lot easier than some other MC games, but there are still moments (many, many moments) where you'll lose through no fault of your own, but as a result of random crap just happening as you close in on the finish line. I've had police cars jump onto me like linebackers, buses and trucks block entire lanes of traffic as a result of my AI opponent sideswiping him, buses that camp RIGHT at the landing point of an almost required ramp jump section and AI foes who will kamikaze themselves into me.
With all that bile dispensed, the game is just perfect in every other area. I love my tricked-out '63 Corvette.
Also, Black for the PS2 is another good pick for me. I used to think I hated the game, but then realized that as much as I sometimes despised it, I couldn't stop playing. I had to admit that I liked most of the game, it was just that certain levels (despite being a lot of fun) could annoy me to no end (Spetriniv Gulag... GRRR!)
Strangely, I've never really been all that frustrated by some of the obvious candidates, like God Hand or DMC3: SE.