Oh boy am I glad to see the amiga get so much appreciation!
I see nobody has mentioned:
I used to love that game! until I lost the manual and I could not play it anymore
As well as all the classics which have been mentioned
My personal favourites were Cannon Fodder, Alien breed, James pond, Zool 1 & 2, Stardust, Speedball 2, Flashback. Ah hell the list is too long :lol
As well as all the free little games that came free with the Amiga mags! some were great! one game called Goblins (an adventure game to do with maths) or something had me and my mate hooked for days and days!
I do remeber Cannon Fodder 2 being so damned hard!! and I thought level 99 of Cannon Fodder 1 was hard until I played that game :lol