Red Faction 2. It's not a great game (especially compared to its predecessor), but because the story doesn't get interesting until half-way through the game, it wasn't until I played it for the second time that I cared about what was happening in the game's first half.

I wouldn't say the game is necessarily better after you beat it, but Silent Hill 2 is certainly different once you've beaten it and can better understand the meaning of the game's imagery.