My current top 12 shoot em ups (doesn't include "tunnel shooters" like Internal Section and Tempest X, or hybrids like Panzer Dragoon and Rez (or even stuff like Geometry Wars) -- those games would all be in my top 12, but this list is for more traditional titles):
12. dodonpachi (psx/saturn) - Simply one of the most intense games ever. Beautiful.
11. zanacXzanac (psx) - Two great games on one disc. While some shooters are "classic" but feel kinda musty, Zanac never lost its touch. The sequel on this disc is even better.
10. border down (dreamcast) - I played this game on my friend Nathan's old Dreamcast to death, and nostalgia for this classic is one of the main reason I bought a Dreamcast for myself.
9. Chaos Field (dreamcast/gamecube) - One of the most underrated games ever! Almost completely comprised of boss fights, but man, what boss fights they are! One of the best soundtracks ever. Just an amazing game, if you take the time to understand its complexities. This is what's commonly known as a "Gamer's game". Only hardcore fans of this genre will "get" the beauty of this game! At first, I was like "hmm.. only boss fights... huhh.. uh..." but something clicked. Everything adds up to a truly beautiful, one-of-a-kind experience... hard to explain, and challenging as hell. But you need to play it at least once.