these games are games i was addicted to in my teens, starting around age 11, in Taiwan. It's when arcade video game just started.
Space Invaders (1978) is one of the first. It was kinda boring and lousy game play, from game design point of view, but was basically the first shoot'em up video game. Before Space Invaders, there's basically just ping-pong.
Asteroids (video game) (1979) is also one of the first video game. However, in terms of design, it is superb, even in today's standards.
Asteroids is a extremely mathematical game, in the sense that the core concept is to predict ＆ control projectile direction ＆ momemtum.
You have 2 buttons for turning left/right. Then, one button for “thrust”. Another button for “fire”.
Defender (video game) (1980)
another best game. Also a game i was very much addicted to. Defender is a bit different than others, in that the control is a bit different and difficult.
normally, in “shoot'em up” video games, you have a 4-way joy-stick to control your ship's motions. In Defender, you have a joy-stick, but it only controls up/down motion. Then, you have a button called “thrust”, which makes your ship go forward. Then, you have another button that reverse direction of the ship. This made the game far more interesting, as well as more difficult.
Then, there's a “fire” button, of course. There's another button “smart bomb” that kills all enemies on screen. Another button named “hyperspace” or something, that transport your ship to some random location, used for escaping precarious situations.
Phoenix (arcade game) (1980) is one of the game i played a lot. Now playing it, it's kinda silly and not interesting.
1942 (video game) (1984)
the game play is very mathematical, similar to asteroids, but more rigid, as there's no momentum involved — your ship moves in any direction in constant speed and immediately corresponding to your joystick.
R-Type (1987). A beautiful game. I've never played it much though, but watched a lot other people play.
Space Harrier (1985). Another fantastic game, one of the first 3D ones. I've not played much.