I play them for part nostalgia, part pick up and play ( like some of the other guys ) and for their artistic nature. Another thing i find bring me back to Amiga games, again and again is the sonics of the games.
Games today sound sonics wise like movie productions and have lost that unique sound that only chip music can bring which seems to have so many variations in style and the samples used. And although i welcomed the era of Texture Mapped 3D to the Amiga in the 90's and the improved chipset of AGA, i didn't quite realise at the time that i did not want my games to feel real years later!
What i realise now is that the sheer imagination and beauty of pixel art in a fantasy kind of world whether it be an Adventure Game, Shoot-em up, Platformer, Strategy..etc.. is what had me captivated, but not today where i step into a game trying to be so real that misses the escapist point of why i played games to begin with. The real world looks and feels stressful enough as it is, why would i want it to look so real in a game!?.. For Graphics!?!?.... Part of the reason why i got or upgraded to any system was for Graphics, but all the above mentioned was why i really played!