I've always been in love with the NES Batman
The music and look of it are so different from any other NES game. It has such a dark and gloomy look and sound, which is just like the original Batman movie, and how I would imagine Gotham City looking if it were real.
The music for Stage 1 is especially awesome:
http://www.vgmusic.com/music/console...es/bm1-st1.mid
I also used to to really like the original Gameboy Batman. It has been several years since I last played it, but it was awesome when I last did.