My most memorable is probably Mario 64. I didn't actually own the console at launch, but I was blown away when I played the game at a preview event prior to the N64 launch and later when I got to play it at friends' houses.
Next up would probably be Soul Calibur for the Dreamcast. It was such a leap in visual quality that my friends and I would just watch the various move demonstrations in Exhibition Mode when we weren't playing.
Tekken Tag and SSX for the PS2 were also extremely impressive and memorable as games that looked remarkably better than the competition.
I didn't get a 360 at launch, but when I picked it up I have to say that Dead Rising was easily the most impressive title for the beginning of this generation just because it was so unique. This generation has, for the most part, been rather unimpressive, but that might be due to the fact that I have been heavily into PC gaming the whole time.