This is extremely difficult...
In no particular order:
Final Fantasy (Series)
Half-Life (Series)
Deus Ex (Or other Irrational games: inc. the amazing System Shock series)
Any Bullfrog Game (Dungeon Keepr and Theme Park in particular)
Any
Introversion Game (Defcon, Uplink & Darwinia)
I am currently playing a lot of STALKER. And I LOVE it, so so very much.
It is a stunningly beautiful game, a very nice concept (I'm not a great fan of RPGs like Morowind because of the fantasy setting) and is in many ways groundbreaking.
The problem with Stalker, though, is that itwhilst trying to be so much, it can only dissapoint. I miss the lack of vehicles and the sleeping mechanism I was expecting, I miss that it's not quite as open as promised, and the missions are limted.
However, the next patch will apparently remove the storyline, and allow missions for all factions. It should make the game much more like what i thought I was buying. That, and a SDK release for the great mods out there will launch it to the top of my list.
I'm also really looking forward to Fallout 3, and Bioshock.
I also have a very, very large soft spot for the Command and Conquer serieas. Not because I'm and RTS fan, but because I play them for the stories and fantastically camp acting.
Silent Hill games are also a big, big fav. of mine...
That about lists the most. there are more (Civilisation, Gran Turismo, Wipeout, the X-Wing series, etc. etc.)
Edit: And DOOM! How can I forget Doom! I was brought up on it...
And Mario Kart
And Super Mario
And Golden Eye!! Oh my god! Golden Eye - damn, there's no space in my top five...
Gah...