You can find rusted/dilapidated versions of most of the in-game cars, but this generally doesn't affect the performance.
Additionally, each of the gang leaders (Maero, Shogo, and The General) have a custom vehicle that's got something special about it: Maero's monster truck has boosted durability, Shogo's prototype motorcycle is exceptionally fast, and The General's Bulldog SUV has a roof-mounted machine gun.
Ace Custom: Almost any vehicle can be taken to a garage and modded for extra engine power and durability in addition to cosmetic changes.