I'll be honest, I'm not a fan of shooters. However, I do like games with shooter elements, like Megaman, Metroid, and (big surprise) Cave Story. I've tried games like Super R-Type and Xevious, but I find that the only true shooters I like are Galaga, Bosconian, Millipede/Centipede (I don't see a difference), Missile Command, and Sinistar.
Galaga is just a classic. You move horizontally to shoot down bad guys, and risk abduction just to get the double-shot. Bosconian is like a roaming shooter, where you fly around an asteroid field and destroy enemy bases while avoiding enemy battle-formations. However, those bases are like miniature Death Stars; they are surrounded by defense units that shoot at you while you try and hit the core by shooting through this tiny hole in the base. They may also release enemy squadrons that run away either if you kill the leader, or all of them.
Sinistar is another roaming shooter, except with this, you just shoot enemies and tackle asteroids for Sinibombs. Rack up as many of those as you can. However, after a period of time, Sinistar (the roaming ship-eating death weapon) begins roaring at you and chases you. If you touch him, he eats your ship. This is where the Sinibombs come in; you have to try and retalliate by shooting the Sinibombs at him to destroy him (takes 20 to kill him.) All the while, Sinistar's ominous voice roars at you; "Run, coward!" "Beware! I live!" "I hunger." "ROAAAAAAAARRRRRRRRRR!" 'Nuff said.
Millipede/Centipede are just awesome. You use a track ball to shoot a string of spheres (Millipede/Centipede) that are linked together and make their way down to you. You just have to shoot all of the spheres off to make the next level. That's pretty much it.
Missile Command is one of the greatest story-telling games ever
(proof.) I love the frantic pace at which you move the cursor to throw out missiles that kill nuclear bombs with an incredibly large blast radius. Plus, the fact that you can strategize using all three of your defense bases, is an awesome thing.
So for my favorite, I'll have to say it's a close tie between Sinistar and Bosconian. I love the roaming shooter idea, but they both have uniquities. Do I like the idea of destroying many stationary death machines with only one weapon, or do I like destroying one mobile vehicle that can kill me on touch that necessitates the hunting of special weapons? I can't decide.