Sega has announced that Golden Axe is available for the iPhone and iPod Touch like, right now. You can hop on the iTunes Apps Store and grab the game for $4.99, and get your Amazon on.
The classic game appears to be fully playable using the touch screen, which is overlayed with a mostly-transparent d-pad and three button set-up. Not sure what you're supposed to do when a dwarf runs off with your magic vile and gets all up underneath your thumb, but I'm sure Sega has it worked out.
Golden Axe for the iPhone/iPod Touch features all of the levels of the original, plus two bonus levels not found in the original.
Surprisingly, the original Golden Axe holds up pretty well after all of these years, and $4.99 doesn't seem to steep. You thinking about picking this one up?