An unexpanded A1200 will run most games. If you want to play 3d games like Breathless, Alien Breed 3D, Nemac IV, etc, you would need at least an 030@50mhz accelerator with some RAM. I'd estimate around 95% of games do not require an accelerator or extra RAM.
An A500 will run quite a lot of games too, but not the ones that rely on the newer AGA gfx chipset as found in the 1200.
