Turok 2: Seeds of Evil (N64)
This game got me into first person shooters, and was overall one of the most badass games I have ever played in my life. Impressive visuals, visceral gameplay, explorable environments, and creative enemies. The awesomeness of this game gave me such an obsession as a kid, and even as an adult. I've done my best to collect comics, action figures, and whatever I can find based around this series, with Turok 2 easily being my favorite.
Metal Gear Solid 3 (PS2)
An immersive game with a great story, solid gameplay, and Hideo Freaking Kojima. This game seriously perfected everything people have come to love about the MGS franchise, and is easily my favorite and most replayable. Like every MGS before it, this game really knew how to mess with your mind a bit, and give you a level of freedom not seen in even most stealth games today.
The World Ends With You (DS)
My god, that soundtrack. This game oozes style, and had combat that I really felt justified the DS touchscreen. I was probably too excited when I found out the characters were in Kingdom Hearts: 3D. The story is a little simplistic, but I think that's one reason I like it so much.
Crysis (PC)
This was the game that got me into PC gaming. Seeing gorgeous screenshots of a game that I thought would never have been possible on consoles, I decided to use my incredibly limited knowledge of PCs at the time to build my own just to see this game for myself. I'm glad I did. This game still looks gorgeous, and I feel has fantastic FPS gameplay. Story is very weak though, this time not in a charming way.
Deus Ex: Human Revolution (PS3)
I'll admit, I never heard of or played the original Deus Ex until this came out. Playing Deus Ex however made me feel so free. The game technically may not have been open world, but the way this game just opens up many ways to complete your objective makes the game feel more massive than it actually is. I also love the visual style. I was immersed in this game start to finish every time I played it, and I won't complain if I ever have to come back to it again when I've run out of my backlogs (assuming I ever do).