I would say EyeToy, Singstar and Buzz, they gave birth to proper casual gaming

This is not intended to simply be a list of good games; it's a list of the most influential ones. If you'd like to argue that God of War, a very well made but totally generic action game was more influential than Parappa the Rapper, the first Rhythm game to spawn dozens of knock offs for over a decade, go ahead. This is basically like arguing that "New Super Mario Bros" is highly influential, by the way. Very well done game with great reviews and even better sales than God of War, but just a generic platformer, all the same. 

Gran Turismo is a worth possibility. It was by no means the first Racing Sim, but it was the first explosively popular one.  

1. Gran Turismo - a great racing game that was the best-selling PS1 title.

2. God of War - it just is.

3. ...I don't really know, I haven't played many games on a PlayStation console.

1. Gran Turismo, GT3 sold extremely well, and with GT3, and more with GT4, got close and closer to real-life looking graphics, whcih wasn't bad for a PS2 game.
2. Singstar, incredibly popular with girls and women in Europe, anybody who has a PS2 and a sister in their family here in europe, most likely has singstar.
3. ICO, not sure really, but was a pretty cool game, even if I never completed it :P