Sorry, the correct answer is Go.
While I love chess as much as the next man, providing he isn’t he long dead Francois Philidor. If we leave this in the electronic games format I’ll have to go with some old school NES games, namely mike tyson’s punch out and RBI baseball.
Computer game: Civ II was good but even on Deity mode you couldn’t ever get the computer to get a good space war going, and turn based is not fun on multiplayer.
Give me Empire Earth or give me pudding.
I agree that Go is probably the best non-electronic game. But a game of Go is quite an investment in time. A good game with similar strategy and subtlety, but much shorter, is Pente.
For electronic, I’ll also have to go with Civ II.
Social. Conducive to conversation. Easy to learn - hard to master.
Chess (screw Go).
You better be talking about the superior original [Atari Lynx version,](Fixed binding error) and not the bowderized Microsoft Games version. 
But as cool as Chips was, I’d cast my vote for Star Raiders. You have to be damn good to make “Star Commander - Class 1” consistently.
(As for pinballs, nothing beats the original High Speed by Williams. But then, most Williams pins are major kickass)
For 2 players - backgammon
For 3-6 players - poker
Bridge.
It’s social, has elements of luck as well as skill. Can be played at an unsophisticated level (“kitchen bridge”) or at a highly skilled world-class level.
There’s a richness of situations, subtleties and possibilities… and it’s fun!
Chess
Half-Life
The various progeny of this game are amazing. Both in multiplayer (Counter-Strike, Team Fortress Classic) and Single player (movie like game play with extensive cut-scenes) numerous expansion packs, and free multiplayer and single-player mods (ie they live 1-3). That’s a great game which revolutionized First player games and a hell of a value for my $29 bucks. 
-me
There are two party games that absolutely rock. They work best if you have a lot of people.
Liar’s Dice (5 or 6 players best)
Pit (7-11 players if you get the more recent playing decks)
Street Fighter 2 Champion Edition
The character design was perfect, the gameplay was insane, and the control hasn’t been duplicated to this day.
I would put Quake 3 at a very close second.
Runners up
GTA3
State of emergency (least till the novelty wears off)
Victory Road
Heavy Barrell
Pacman
Super Mario World.
World Eater
I have Street Fighter 2 Champion Edition arcade game in my living room, I love that on the front it says
NOW WITH THE ULTIMATE FEATURE!! Play as the same character at the SAME TIME!!!
SiN
Single-player untouched by any other FPS and a multiplayer game that had me hooked for two and a half years. I even go back to the multiplayer every once in a while and it hasn’t gotten stale with the changing times. It had an amazing CTF game, incredible level design from the innovators at Ritual Entertainment along with a great little community that put together some of the greatest maps I’ve ever seen amateurs create. The story line didn’t take itself seriously, but still allowed an immersive game with good plot twists. I’ve never played a game that had such weapon balance. A good player could win an MP game with whatever weapon was suitable for his situation.
Its initial release was marred by some game crashing bugs, but a patch that was released in a week or two fixed those and further patches added cool features and new maps. Its release was overshadowed by Half Life a couple weeks later. I played Half Life’s single player game all the way through and tried its multiplayer, and I really didn’t see what the fuss was about. Of course I was kinda biased, I had been playing Sin for the past couple months and was used to its great, innovative gameplay.
I’d also have to say that its Mission Pack Wages of Sin is the greatest mission pack ever released also. In addition to a whole new single player game that lived up to the original, it added more innovative weapons, multiplayer modes, and even the first intuitive multiplayer vehicles in an FPS.
If you ever see Sin or Wages of Sin in a bargain bin or at a friends house, please give it a shot, you will be glad you did.
I agree with Bridge, for reasons already named. Seems so simple, but the more you learn, the more you realize is still to be learned.
Computer/Single Player: Gonna go with the crowd here too and say Civ2. Near-infinite replayability. But I had to divide this category because for a true “best game” experience, it has to be interactive, i.e. multiplayer.
Computer/Multi-Player: Starcraft. The depth and richness of strategy in this game is truly stunning. It never gets old, and it’s pure competition.
The best game ever is Texas Holdem no-limit poker. period.
SUPER MARIO 3.
Dare to disagree with me, and I’ll clobber you with my raccoon tail.
And the absolute best four-person card game is not bridge, nor is it poker, 'tis EUCHRE. (Eh?)
Board - Settlers
Card - Poker (Texas Hold 'Em)
Card Based Strategy - Magic: The Gathering
Console Video - Final Fantasy 2 (Or 4 if you live in Japan.)
Computer Video - Any Half Life Mod
Sports - Racquetball
Drinking (Random) - Jenga
Drinking (T.V.) - Newhart
Drinking (Movie) - Star Wars
Drinking (Card) - Hurricane
Just MHO.
Going solo: Civ 2
Going non-solo: D&D
Hide the Salami