3. Grand Theft Auto III (PS2)
GTA III was arguably the most talked about game of 2001/2002. It was controversial, because you could pick up a prostitute, have sex with her, and then murder her to get your money back, all on top of the random maniacal rampages that are a GTA standard of course. But ignoring that controversy, it was an excellent game at its heart.
Today, sandbox games often get accused of being repetitive. This could not be said of GTA III upon its release, mostly because this was one of the first games of its kind, so it was all new and fresh. Others will place Vice City and San Andreas above this game, but I disagree, as without this one, those two wouldn't exist.
You don't even have to play through any missions to fall in love with this game. You can just drive around the city and explore, notice a ramp or something, and fly off it to see what would happen. Sure, you could do the same in the first two GTA games, but the topdown perspective didn't give the same sense of exploration that you could get with a 3D engine, so this one delivered perfectly in that respect.