hmmm, very hard to say. I'm probably forgetting A LOT. Some of these are kinda old.
For story, probably Metal Gear Solid on PS1. And Ico for ps2.
For gameplay it's definitely Simpsons: Hit and Run. And probably the sims(for pc, the ps2 sims wasn't so hot-mostly because of the furniture limit-in my bedroom i can only have a bed and that's it)and Worms 2 for pc.
For replayability(and sound!)it's Vice City.
For FPshooters, either Medal of Honor(I love to shoot Nazis) or 007 Nightfire.
For racers, GT 3. I haven't played the new Need for speed but I think it looks good. More customization options than GT 3.
And this is random but for best golfing game it's Tiger Woods PGA tour 98(I think) for the ps1. On two player you can taunt the other player. i wonder why they never kept that option?
But I can't say for sure what the best games are. I don't have an xbox or a good computer so I can't say I've played Halo or any other games ppl talk a lot about.