Alien Swarm

Great variation on the Galaxians/ Space Invaders theme. Very addictive, I seem to recall as a 12 yr old!
The spinny thing on the end of the "eye" would eventually fly off and try to hit you, I recall- it would get extremely frenetic by this point!

This is a seriously good game, with a genius scoring system. The aim isn't to protect your ship, but to protect you energy reserves. Graphics are great - time of writing, my high score is 46,000.

More tips: you can carry five ammo units at a time, but only carry two (so if you die, you don't lose the ones you're carrying). And to shoot the annoying "darts," the best way is to wait until they're very close, shoot, then immediately move away; they have less time to dodge at close range. Finally, you get one ammo point for every 100 points you score. Eventually the eye-line grows a spinning thing on its tail, but I always die before I see what it does.

In case you're wondering: push the joystick up to pick up more ammo; you get more points for shooting two aliens together, or for shooting the "eyes." If you die, the remaining ammo is counted up (not including any you are currently holding), then five ammo points are taken away; if you reach zero, game over. When you destroy aliens you get more ammo points; ideally you'll shoot as many as possible, use up all your ammo, and not die. In later levels, annoying "darts" spawn if you shoot the red line of the "eyes." You can kill them best by firing rapidly when they're close to you, but this is dangerous...just try not to shoot the line.

This game is incredibly fun, and the nifty graphics don't hurt either! Shoot the aliens while trying to protect your ammo storage. Simple, but effective.