Asteroids by Atari, created by Ed Logg and Lyle Rains. Original arcade release in 1979.
A classic among classics, Asteroids was one of the early "huge hit" games which made a notable impact on culture, for being particularly hi-tech (for the time) and also possessing relatively unique gameplay.
The game was extremely notable for its distinctive vector-drawn graphical style (most arcade games use raster graphics technology, with elements created out of pixels; vectors use brightly-lit lines of light).
The game itself was fairly simple - thrust, shoot, and dodge. Your playfield wrapped around vertically and horizontally across the single screen, and everything which passed offscreen in one direction would appear on the opposite side. The action was frenetic, with several obstacles and enemies constantly threatening your existence. Also a luck-of-the-draw "hyperspace" feature was accessible, for a last-minute ditch to try to save your skin if you were about to be nailed.
It looks primitive now, but Asteroids is one of those games that contains such a purity and accessibility of gameplay that it still remains an enjoyable challenge to this day.