If you wanna be real technical about it; GTA III, GTA: Vice City, GTA: San Andreas (all of which are better games than Saints Row), GTA: Liberty City Stories (which is not), The Getaway (also better), The Getaway: Black Monday (also not better), The Simpsons Hit and Run (which is), Driv3r (not), Driver: Parallel Lines (not), Driver 2 (not, but close), Driver (not, but close), The Godfather (better), Scarface (better), Mafia (not so much better on the PS2), True Crime (better) and True Crime: New York City (about the same).
Saints Row sure as hell isn't anywhere near the top of the genre, regardless.