Can't choose one (but I will) since I've played so many after owning an Amiga, Snes, Megadrive, Lynx, ST, Speccy and Vic-20.
Highlights of shoot em ups I've played and thought were great games:
Vic-20 - loved Gorf and Omega Race
Speccy - lightforce and others I can't remember
ST - Plutos! and Asteroids which came free with the system disks! Also OIDS, I loved this game, but I'm not sure if it counts
Lynx - that one with the eyeballs but can't remember it's name, er, oh yeah - Gates of Zendocon!
Megadrive - Gynoug, Areoblasters
SNES - Super Aleste
Amiga - loved 2-player blasts - silkworm, battlesquadron and banshee.
The best of all time may not be here and I will have missed a few but these are the ones I remember playing the most off the top of my head.
Out of the above, Super Aleste goes forward as my fave blaster.
Rck and others, if you liked Axelay and the R-type series on the snes (and I love them games two) you're going to love Super Aleste assuming you haven't already played it!
Super Aleste really shines in the gameplay department. It is the best I have ever experienced in a shooter and I've played a lot of games. Tons of powerups and weapons, not to mention 6 different power levels for each of the 8 weapons AND several modes of fire on each individual one! Using the correct mode of fire and selecting the best weapons for different circumstances is quite a skill and means your constantly thinking as your blasting. Also the control is TIGHT! I mean this is some of the most responsive control I have ever played. And believe me you are gonna need it to avoid the massive enemy fire. Take my word for it you will not be dissapointed with this game and you guys must try it out some time on an EMU.
Goes to find screen shot.............................