I've been working on a list of coin-op/arcade game "firsts" as they apply to video games (not electro-mechanical arcade games) and have compiled the following so far.
Anything missing? Anything you would dispute? Also note that there are some unanswered questions at the bottom, if you have the solutions, please send 'em along.
Computer Space (1971, Nutting): first arcade video game.
Pong Doubles (1972, Atari): first arcade game to allow 4 player simultaneous play.
Gotcha (1973, Atari): first maze video game.
Gran Trak 10 (1974, Atari): first driving video game.
Tank (1974, Kee Games): first arcade game to use ROMs and have solid sprites.
Gun Fight (1975, Midway): first arcade game to use a microprocessor.
Death Race (1976, Sharp Image): first arcade game based on a movie (though it wasn't "licensed"), Death Race 2000.
Computer Othello (1978, Nintendo): Nintendo's first arcade game (distributed in Japan).
Space Invaders (1978, Taito): first game to keep a high score between games (until the machine is shut down).
Space Wars (1978, Leijac): first vector game.
Gee Bee (1978, Namco): Namco's first arcade game.
Atari Football (1979, Atari): first game to use a trak-ball controller.
Galaxian (1979, Namco): first arcade game to use all color sprites.
Head On (1979, Sega/Gremlin): first "eat the dots"-style maze game.
Warrior (1979, Vectorbeam): first head-to-head fighting game.
Pac-Man (1980, Namco): first animated main character.
Battlezone (1980, Atari): first game with an interactive 3D environment and first-person perspective.
Star Fire (1980, Sharp Image): first arcade game featuring a cockpit-style cabinet.
Star Fire (1980 Sharp Image): first arcade game that allowed you to enter your initials for a high score.
Stratovox (1980, Taito): first game with speech synthesis.
Defender (1980, Williams): first game to feature a world where things were happening off the playscreen.
Space Invaders Part II/Deluxe (1980, Taito): first game to include an intermission ("SOS").
Berzerk (1980, Stern): first game to be blamed for someone's death when in January 1981, 19 year old Jeff Dailey died of a massive heart attack while playing the game.
Tempest (1980, Atari): first arcade game to use color vector graphics.
Centipede (1980, Atari): first arcade game to be designed by a woman: Dona Bailey (with Ed Logg).
Zaxxon (1982, Sega): first arcade game to employ an isometric "3/4" view.
Journey (1983, Bally/Midway): first game to use digitized graphics.
Astron Belt (1983, Sega): first laserdisc game.
Dragon's Lair (1983, Cinematronics): first animated laserdisc game.
NFL Football (1983, Bally/Midway): first arcade game to accept dollar bills.
I, Robot (1983, Atari): the first arcade game to use 3D filled polygon graphics.
Cosmic Chasm (1983, Leijac): the first home game to be converted into an arcade game.
Firefox (1984, Atari): first to use actual movie footage in a game.
Psycho Soldier (1986, SNK)): first game to feature a fully digitized vocal soundtrack.
NARC (1988, Williams): first 32-bit arcade game (TI 34010).
Exterminator (1989, Gottlieb): first arcade game to use 100% digitized graphics.
Hard Drivin' (1989, Atari): the first driving game to use 3D polygon graphics.
NBA Jam (1993, Midway): first sports-licensed arcade game.
FIRST LIGHT GUN GAME?
FIRST TWIN STICK GAME? Tank?
FIRST SEGA ARCADE GAME? (1973) Hockey TV? Pong Tron?
FIRST STEREO SOUND? 1975, Jet Fighter? Destruction Derby?
FIRST COMPUTER GAME TO ARCADE? icwhen.com says Choplifter (1985, Sega), klov.com says Lode Runner (1984, Irem)
FIRST GAME WITH A JUMP BUTTON? Donkey Kong?