Overview
Pong is widly accredited with being the first ever computer game, although this is actually false - the first being "Spacewar" programmed in 1962 by MIT student Steve Russell. (actually if you want to be pedantic, in 1958 Willy Higinbotham rigged an oscillator to 'play' something called tennis for two, but as for being a game, well...thats debatable).

That aside, Pong is what most people think of when asked what the first ever computer game was, and that's close enough for us.

History
In 1972 Atari was founded, and they created the first ever arcade game, Pong. Named partially because of the sound the ball made when it hit the side, but mainly because Ping-Pong was already taken.

As a test, the very first pong machine was placed in a local bar (Andy Capp's in Sunnyvale, California). Here is an account of what happened, from the book "Zap: A History of Atari's Rise and Fall":

"One of the regulars approached the Pong game inquisitively and studied the ball bouncing silently around the screen as if in a vacuum. A friend joined him. The instructions said: 'Avoid missing ball for high score.' One of [them] inserted a quarter. There was a beep. The game had begun. They watched dumbfoundedly as the ball appeared alternately on one side of the screen and then disappeared on the other. Each time it did the score changed. The score was tied at 3-3 when one player tried the knob controlling the paddle at his end of the screen. The score was 5-4, his favor, when his paddle made contact with the ball. There was a beautifully resonant "pong" sound, and the ball bounced back to the other side of the screen. 6-4. At 8-4 the second player figured out how to use his paddle. They had their first brief volley just before the score was 11-5 and the game was over.

Seven quarters later they were having extended volleys, and the constant pong noise was attracting the curiosity of others at the bar. Before closing, everybody in the bar had played the game. The next day people were lined up outside Andy Capp's at 10 A.M. to play Pong."

What followed is, of course, history. Atari would go on to become one of the most successful games companies around, then fall into hard times and die a lingering death. Pong was the first of their great successes, and judging by the re-releasing of it with jazzed-up graphics onto the Playstation and PC, it's still remembered fondly even today.

Models
There was the original arcade machine... and then, there was the home machine. Atari would go on to produce further versions of Pong involving multiple variations, and up to 4 played (this version was dubbed "Pong Doubles"). They would produce even more versions through a licensing agreement with Sears, who released Pong through their "TeleGames" lable.

Legal footnote: "Zap! The Rise and Fall of Atari" is copyright Scott Cohen. It sounds like quite a cracking book, you could probably pick up a copy from amazon.com, in fact, I've done all the researching for you, it's right here

Other footnote: Although it may prolong the memory of Pong, Hasbro's "Pong: The Next Level" is a truly horrible game. May a curse forever be upon them.

Final footnote: I'll shut up now.