Top fives are boring. These are the games I keep returning to.
Daggerfall (PC) - Good old buggy Daggerfall, with its rich, vast world to explore. You'd think I had played it to death by now, but I'll likely never be finished with this game.
UFO: Enemy Unknown (XCOM: UFO Defense in the US) and its sequel Terror from the Deep (PC) - I just love it. I love killing sectoids, I like how you capture alien technology and develop better weapons, I love how you have to perform to a certain standard to keep your funding, and I love how in end-game you can mind-control all the enemies and have them drop their weapons and turn their backs to you to be executed the next round. XD
Might and Magic VI (PC) - I play through this game at least once a year. I love the story, though it would have been greatly improved by a proofreader - there are a plethora of typoes and grammatical mistakes in the game texts. I also like VII and VIII, but I don't play those nearly as often as VI.
Final Fantasy Tactics (PSX) - ok, it's been years since I last played this, but I know I'll play it again once I have lots of spare time. I love the system, the world, the characters (even though they have no noses), and Ramza's butt in the last parts of the game.
Elite II: Frontier (Amiga/PC) and its sequel First Encounters (PC) - this game really fueled my love of outer space with its star maps partially based on real data. Love, love, love this game, with its openness and total freedom of choice. I just wish you could actually go to Beta Lyrae without the game crashing. I want to see a contact binary! I have fond memories of getting too close to a white dwarf star (Sirius B, was it?) to pull away, being hopelessly caught in its gravity, and having to do a hyperspace jump to escape. It was so pretty up close! And the advertisements in the space stations, such as "Recycle or die!" and the various non-profit organizations you could donate money to, of which I only remember my favorite, "Ban military drives now" (military drives take up less space in the vessel and require smaller amounts of fuel, but use military grade fuel which is more expensive than regular, and leaves you with radioactive waste after use).
Black Crypt (Amiga) - Classic dungeon-crawl with a good, generic backstory. I've never completed the game, but I hope to be able to soon.
I'm also very fond of the Monkey Island series, though I have only completed the first two games on the Amiga. I actually own those, but I have no idea where my originals are. They might have been lost for all I know. Guybrush Threepwood was my first crush.
Of not-so-old games, Katamari Damacy and its sequel We Love Katamari (both for PS2) deserve mention. They are insane and if you have not tried them, you ought to.
I have a feeling I might add Portal to this list if I ever get to play it.