Wow, it's an interesting question once you start to think about why you would want to forget a game and play it again "for the first time". In my mind, it warps the question into "What game had a better first experience than any other time you replayed it."
Sifting through the thread and seeing some of the suggested games that I have played (Chrono Trigger, FF VI, FF Tactics, Halo, Half-Life, System Shock 2, GTA 3, Shadow of the Colossus, etc...) reminded me that re-playing the games after beating them had no ill effect on it. My second time, or third time, or fourth time through the game was not as enjoyable as the first, but it didn't really suffer at all either.
And this led me to my choice: Demon's Souls.
That game is a whole different monster when you know absolutely nothing about what is around the next corner. The game hinges on your ability to remember things: Monster locations and patterns, trap and item locations, boss tactics, and general stratagies for just surviving. Each moment becomes this super-tense "Oh god what is around the next corner" moment. Each new enemy causes you to get really scared because you don't know anything about it. Each new boss is basically a death sentence unless you manage to figure him out quick (I beat "Old Hero" on my first try!). I have tried to go back and re-play the game countless times, but find myself giving up after beating the first area, even when trying a radically different character build. Every time I load up a zone to try, all I think about is how completely awesome it was exploring the level the first time, and how now I just run past traps that used to scare the hell out of me.
It's the only game that's ever done that to me, which I find strange.