1. Counter-Strike: Source
2. Mass Effect 1
Mass Effect was the best combination of story, role-playing, graphics, and immersion that I have ever played. Mass Effect 2 actually received more critical acclaim, but it couldn't touch ME1 in my opinion. When the final song kicked in during the credits, it gave me chills. (The song is M4, Pt. II by Faunts. You can see the credits and song here.)
3. Half Life 2
The original Half-Life was revolutionary. And I had a hard time deciding if I wanted to put HL1 or HL2 here. But HL2 did the impossible - supplied a story as good as HL1, while improving the graphics, providing awesome and original weapons (has any weapon ever been more fun than the gravity gun?), and left you wanting more. Wherefore art though, HL3?
My second most-played game after Counter-Strike. The story was solid, the characters were great, and the setting beautiful. And with so much additional content, side-quests, and user-created mods, the fun just kept coming for years. Here is my ranger, Juliette, standing on a cliff over the city of Whiterun.
5. S.T.A.L.K.E.R. - Call of Pripyat
The STALKER series is definitely the dark horse of the bunch. All three were great, but I loved the second installment the best. From the quirky Russian story line and characters, to the eerie and infamous setting, along with the unexpected RPG component, the game was one of the best. This one actually had me afraid to look around the corner...
6. Dragon Age: Origins
Another great story-based role-playing game in a unique and believable fantasy setting. Dragon Age had story, characters, and romance! Normally I'm not a big fan of third-person perspective, but it really works here.
7. Banner Saga 1
I did not expect to like this game as much as I did, let alone have it become a top ten favorite. It is not very complex, and utilizes basic graphics. But it all works, with a fantastic story, a wonderful setting, and engaging races and lore. And some tough choices lead to permanent deaths. No Hollywood endings here!
8. Deus Ex
Deus Ex is just a great all-around game, adding stealth and adventure to the exceptional RPG components. The player has a myriad of choices to solve a problem, with none of them being "right" except the one you choose. And any game that quotes G.K. Chesterton is totally legit in my book.
Infocom had a huge run in the 80's creating computer games with no graphics at all. Just text read like a book, with the player changing the course of the game by typing basic commands. Zork is the most famous, but I loved Planetfall the best. The game was comedic genius, right up to the moment when I suddenly found myself bawling. And I wasn't the only one.
10. Lords of Conquest
Oh, the hours we wasted at college on LOC! Most games on this list are story-based, but it is bookended by two games that work best when played with another human. LOC is a strategy game with a depth that is masked by its alluring simplicity. Unfortunately, the most recent version we have is a crappy DOS-based version; the game is in desperate need of a modern overhaul.
So, what's on your list?
System Shock 2 (Windows)
Command & Conquer: Red Alert 2 (PC)
Operation Flashpoint: Cold War Crisis (PC)
Wing Commander III (PC)
Speedball 2: Brutal Deluxe (Amiga)
David's Midnight Magic (C64)