Impossible Mission (1984)
One of the first games I ever played, and likely the earliest action-roguelike. The unarmed player has to dodge robots as well as a floatin ball taken from the cult TV serial The Prisoner. You move through a randomly generated set of rooms, inspired by Rogue. You have 6 hours to beat the game, and for each death, you loose ten seconds (I had no clue of this at the time)
https://www.youtube.com/watch?v=ivHFP3dJAkM Robotron 2084 (1982)
The most pure and intense twin-stick shooter. Sadly I never played it on the arcade, only on the PC port.
https://www.youtube.com/watch?v=aOVA2Axxfdk Prince of Persia (1989)
Harsh, stylished platformer with stellar animations.
https://www.youtube.com/watch?v=Xv20j8ChtRY SimCity (1989)
I never played this one, sadly.
Tetris (1985)
A simple formula that just works.
International Karate (1985)
Player-vs-player karate game. Unlike later brawler games, such as Streetfighter or Mortal Combat, the fighting isn't dependent on convulsed button combinations. Instead, you simply can move the joystick in 8 directions with or without the button, resulting in a total of 16 moves.
Bubble Bubble (1986)
Upbeat single-screen platformer with a shitload of levels, each one with its own design and physics.
https://www.youtube.com/watch?v=BuXOSBb4hQw Bubbles (1982)
Widely ignored, but a solid game nonetheless, with unique floating physics. Like Pacman, the gameplay is centered around eating everything and avoiding getting caught.
https://www.youtube.com/watch?v=BuXOSBb4hQw Kaptajn Kaper in Kategat (1985)
Classic danish roguelike pirate sim, writen in BASIC. Rather dated, but easy to get into.
You can play the english version at my collection
The Shareware Motherlode, as well as some other early games.