The SNES/ Super Famicom has a small but excellent selection of shoot 'em ups.
Some of these include:
Axelay (Konami masterpiece)
Area 88/ UN Squadron (Capcom's finest 2D shmup)
R-Type III: Third Lightning (best R-Type ever, simply amazing)
Super Aleste / Space Megaforce (brilliant Compile game, much better than the mediocre Musha Aleste)
Macross Scrambled Valkyrie (one of the finest shmups ever, tons of sprites on screen with no slowdown, trounces over the average PCE & Saturn Macross games)
Flying Hero
Sonic Wings / Aero Fighters
Gokujou Parodius, jikkyou Oshaberi Parodius and Parodius Da
Cotton 100%
Pop 'n Twinbee
Gradius III
BioMetal
Kidou Soukou Dion / Imperium
Super Swiv /Firepower 2000