Battle Squadron

I cannot speak for the quality of the game myself, but this game is highly regarded in both the Amiga and shooting game communities. This was developed by the team who worked on Hybris (another game on the list) and is said to improve the gameplay in most every way. The common consensus is you should try and experience the Amiga version; the Sega Genesis version is inferior.
Gameplay only has one music track, but the game over theme is great.