One such game was Galaga, not to be confused with the similar game, Galaxian. Once a Space Invaders loyalist, I've come to appreciate Galaga, especially in its incarnation on the Atari 7800.
The idea is simple - shoot all the Galaxians with your command ship. There are three different kinds of aliens - flagships, hornets and drones. Flagships have to be shot twice to be destroyed. But there are enough little elements thrown in the game that make it really fun.
For starters, the aliens don't just all appear on screen all at the same time - they come streaming out from different directions before going into formation. In later levels they will fire at you as they come out, and in still later levels extra ships that come out will turn and dive at you.
Making Galaga different from Space Invaders is that the aliens will dive at you - they're worth more points if shot while attacking rather than lined up. Flagships will come down with escort craft - the more you shoot, the more points you get. If you don't destroy them on the way down, or if they don't collide with you, they rejoin their fleet.
You can increase your firepower by allowing a flagship to capture one of your ships with its beam - just make sure it's not your last! To get it back, destroy the kidnapping flagship while it's attacking - your liberated ship will spin around and then dock with you, giving you double firepower! Just be careful not to destroy your own ship! I always let one of my ships be taken on the first wave, allowing a flagship I've already hit once to take it so I can then destroy it with just one shot.
Having the extra firepower really helps on the challenge stages - which first appears after the first two waves of attack and then after every third wave. Five groups of eight ships fly in various patterns. You get 1,000 to 3,000 point bonus for destroying groups of eight ships and a 10,000 point bonus for destroying them all. If you don't get them all, your bonus is 100 points per ship.
This is a one or two player game with three difficulty levels. The graphics are good, with brightly colored aliens, and there are plenty of excellent sound effects.
This is a game I find myself playing again and again. It's among the 7800's arcade translations that can still be enjoyed today.