My complete list would probably be too long, so I'm just pointing out the most important and a few of the most recent ones.
Double Dragon (Arcade) - This is the most memorable game from my childhood. And it's amazing how they did everything so perfectly for the time: the gameplay, the music, the graphics, the flawless transition between stages, everything about that game is perfect to me. Well, except for the crippling slowdown.
Street Fighter II (arcade) - The first fighting game I remember that was perfectly put together. So fun and addictive to play, and the original World Warrior version is still my favorite. I still go back and play it every now and then.
SotN - The first game that really sucked me into the PS1, and revived my interest in the series (I had just forgotten about it until this came along). An absolute masterpiece.
Metal Gear Solid - Another game that revived my interest in a forgotten series. So addictive, and the storyline was the best and most involving that I experienced at that point, hands down. I made a deal with my girlfriend that if I play her Onimusha next, she'll have to play this one, because it's too good of a franchise for anyone to go without experiencing.
Bioshock - To me, this game is an absolute work of art. Although it's no tactical shooter, the combat is certainly adequate, and everything else is just perfect to me. I always love games this deep...ones that really leave you thinking. But I love the MGS series, so it was probably a given that I'd be hooked on this one.
Other than Bioshock, Contra 4 has actually impacted me quite a bit lately. I forgot how fun it can be to conquer a seriously tough game. And the great thing about it is how it seems impossible at first, but then with time you can master it completely. It's the pinnacle of twitch gameplay for me. I've always been awesome at Contra, but I usually suck at shmups.