Though many, many, many people believe that Atari's PONG was the very first commercially available arcade machine, it is predated by a handful of other games. Though the case could be made for games like Spacewar!, the truth is that it and other very early "arcade" games were only available to various universities and really never made it into the private market.
The first widely available arcade game was Computer Space, created by Nolan Bushnell and Ted Dabney and released by Nutting Associates. The game came out late in 1971, predating PONG by several months. The game play was similar to Space Invaders and Asteroids; you were a ship trying to dodge enemy fire from a pair of flying saucers while trying to fire missiles at them to destroy them. The goal was to have more points than the computer AI in 90 seconds, if you achieved this goal, you moved onto the second and only other round dubbed "hyperspace" when the screen would switch to a photo negative-esque version of the map.
So why haven't more people heard of Computer Space? It still received a fairly limited run, less than 2,000 cabinets were supposedly manufactured. It also had, at the time, a rather intense learning curve and as such, it was not successful in numerous venues including bars. It should be noted that Nolan Bushnell and Ted Dabney both went on to found Atari, Inc. the next year.
Computer Space was featured in the movie "Soylent Green" (Soylent Green is PEOPLE!) but never made much of an impact with the general public.