For that purpose, there is no better place to start than Spacewar!
Spacewar! originally sprang to life from the mind of Steve Russell, a student of MIT and a member of the school's Tech Model Railway Club(TMRC). Before the time of computers and readily accessible consumer electronics, groups like the TMRC were havens for individuals with a passion for how things worked. Members were known for their desire to see how systems interacted, right down to the nuts and bolts. And when the group discovered and old IBM computer in one of the basements of MIT, they took to it like fish to water.
Evidently other users had built some basic kaleidoscope programs to demonstrate the ability of the display, a fact that left Russell disappointed. Here was a digital display with so much potential, and damn it all if he wasn't going to use it. The idea of creating an interactive game using the technology appealed to Russell, and as a longtime fan of sci-fi, space was the natural starting point.
Encouraged and aided by his fellow club mates, Russell went ahead and designed one of the first video games ever, Spacewar! The first version of the project personally took him about 200 hours, and was completed in 1962, a full decade before Pong came around and truly popularized video games in North America.
Feeling similar to Asteroids - a much later development - Spacewar! was a two player game, as processing power at that time didn't allow for any computer controlled opponents. Players were put at the helm of two spaceships, nicknamed 'The Needle' and 'The Wedge' for their distinctive, if not all that detailed, appearances. Players would control the orientation and thrusters of their spaceship as they maneuvered around the field, trying to fire rockets at one another while avoiding the gravitational pull of the sun.
Simple in concept, but absolutely groundbreaking for it's time.
What they didn't know is that it would soon spark the beginnings of a multi-billion dollar industry.
Nutting Associatates was one of the early pioneers in the coin-operated arcade game industry, having released The Computer Quiz, a computerized trivia game, in 1965. But in 1971, Nutting Associates hired a young individual with an idea to bring Spacewar! to an arcade format, calling it Computer Space(they were clever people back then). Nutting went for it, selling 1500 units of Computer Space, a moderate success when compared to other existing games such as Pinball. The project didn't exactly sell the public on video games as a medium, but it was an important introduction to the industry for the individual who created it.
That individual was Nolan Bushnell, future founder of Atari. Now, I don't think I need to tell you just how much impact Atari had on the games industry.
So there's a little blast from the past, and a small look at the grassroots of our industry. It's interesting to see how much impact can be made by a couple guys, a computer and the question of "Wouldn't it be cool if...".
Sidebar: If you want to see Spacewar! in action, check out this PDP-1 emulator here.