For computer games that can last for a while, here are my choices:
Wing Commander II - I've played a lot of Wing Commander games: 1, Secret Missions 1 and 2, Wing Commander II, Special Operations 1 and 2, Wing Commander Academy, Wing Commander Armada, Wing Commander III: The Heart Of The Tiger, Wing Commander IV: The Price Of Freedom, Wing Commander V: Prophecy (Original and Gold), and I even gave Wing Commander: Privateer a little bit of a try. But of all of them, there was none with the drawing-you-in story of Wing Commander II. Plus, at the time, ships like the Broadsword with sets of guns on all four sides made things truly interesting. No, the graphics weren't as good as those of III, IV, or V, and the characters weren't live-action actors, but it was Wing Commander at it's best. Also - on Wing Commander 2, the keyboard controls were fantastic - you didn't really need a joystick to play. My favorite ship: The Broadsword.
Star Control II - This is another game I got Skander hooked on. Part of what made this game fantastic was playing against a friend - both of you hovered over the one single keyboard trying to blast the other guy out of the cosmos. Funny little races with crazy cultures and ships that truly had a flair of personality. You could tailor-make your own fleet to go up against a friend. Every ship had a ship that was tailor made to take it out, and every ship had ships it was perfect for killing. (Just so it's said, if you're ever in combat with a friend, make sure you have a Thraddash, an Utwig, a Chmmr, and a Spathi. After those four, it's at your discretion. Use the Spathi on the Utwig, the Thraddash on the Chmmr, and the Chmmr on the Spathi - although that can sometimes get ugly.) StarCon2 offered the best of the single player game, and the best balance for multiplayer. StarCon3 then came out, and wrecked the series - turning a classical battle of good and evil into a tale of political correctness and "Can't we all just get along?", while re-telling all the best jokes from StarCon2 (and they're not as funny the second time around). Worst of all, StarCon3's animated figures were *AWFUL*. My favorite ship: The Spathi.
Sim City - There's nothing like building something you might actually be able to envision. A city, with elements placed to your liking? Talk about cool. Oh, there are problems here and there with the original - like restricting buildings to a general commercial, residential, or industrial - but it's a great game for starting out. I've not tried later versions, but the original was a true classic.
Lords Of The Realm II - This game is Braveheart battles on computer and I have to give Skander props for introducing me to this game. I like the sheer simplicity of the game. While Skander wants lots of customization and lots of options and lots of complexity, I like being able to sit down at a game and understand its nuances quickly - which is why I've never gotten into Starcraft, WarCraft, Total Annihilation, etc. Also, I like being a ruthless dictator that sacrifices mercenaries so that you don't have to keep paying them.
Civilization - This is another series I introduced Skander to. I've played the original to death, and I started a game of Civ 2 one time over at Skander's, but I've never even opened up Civ 3, even though I've got it. Again - a simple game, easy to understand, easy to get going quickly. My favorite unit: my "diplomatic" catapult corps.
Other classic favorites:
Star Trek: Birth Of The Federation (if I'm playing any game, this is probably it)
Populous
The Sims
Need For Speed: Hot Pursuit
Microsoft Flight Simulator
The Incredible Machine
X-Wing vs. TIE Fighter (I serve the glorious vision of Emperor Palpatine!)
And then, there are the "short" games - games that it takes less than an hour to play - some of my favorites are:
Welltris (Tetris played from all four directions)
Lemmings
Sherlock
Diplomacy (the original isn't a challenge, but the new version CRAWLS)
Tank Wars (a precursor to Scorched Earth)
And then, there's the arcade:
Tournament Cyberball - I actually have an original Cyberball machine in my house. I played Cyberball for hours when I was younger. Loved the game because there was an element of competition to it, but not tons upon tons upon tons of special key combinations to memorize and master.
Pigskin - if you've got Mame on your PC, grab a copy of this one. Football - played by cavemen - with some carrying concealed weapons.
Defender - a true classic. I was never really any good at the game, but I loved it.
Tempest - there's something about me and unusual controls. I truly enjoyed this old classic.
Battle Zone - old stick vector graphics. I can't really say why I like this one so much, but it's a great favorite.
You'd also find me playing:
Mystic Marathon
Venture
Crystal Castles (affectionately renamed "Run, Bear, Run!")
Donkey Kong
Galaga
Space Invaders
And finally, I have to bring up one of my personal favorite games, just based on the entire experience of playing:
Virtual World's BattleTech
You get into a POD, where you command a mech in battle with up to seven friends. The level of experience is customizable in the pre-game - are you new to the game, or have you played many times before. The various mechs are different, so you can surely find one to your style (I like an Atlas - big, heavy armor, good guns, slower than molasses). Blast your friends! Tower triumphantly over their burning corpses...er...mechs!
This is essentially the MechWarrior game with a "big" feel to it, because when you climb into the pod, all you see are controls and visual and radar screens. That feel is what really sells the game.
It used to be at some of the Dave and Busters places, but they pulled it out.
