Centipede (Millipede is featured here as well) was developed by Atari and released in 1981. Along with Pac-man, this game was as popular with the ladies as it was the guys. In Centipede, the player was a gnome like creature at the bottom of the screen which was moved up and down, and from side to side, with a track ball. The goal was to destroy the centipede coming down from the top of the screen, with laser shots, before it reaches the bottom. When the centipede encounters a mushroom on the screen, it reverses direction, ultimately speeding up its decent. When it encounters a mushroom that has been poisoned by a scorpion, its decent is greatly accelerated. When a section of the centipede is hit with a laser, that section turns into a mushroom, and the centipede then splits in half and continues down. The player loses a life when the hit by the centipede, a spider, or a flea.
There were a number of spin-offs and home versions of this game over the years, including the Atari 2600 version. In the arcade, you might have run into similar, less popular spin-off versions like Jackler (1982) or Slither (1982). In 1982, Atari released a sequel to this game called Millipede. Millipede was, for all intents and purposes, the same as Centipede, except there were other creatures, such as a Bee, Earwig, Beetle, Dragonfly, Mosquito, and DDT bombs.