The game Overlord on the NES had the best intro music of the generation, IMO. It was a port of Supremacy from Amiga and other PCs. The Commodore 64 version had really great intro music too! (I love SID music and warez chip tunes) The Commodore intro melody was later used in a Machinae Supremacy song.
I really enjoyed the game StarTropics too. It had real world tie in stuff with physical media (anti-piracy, but it was neat), and I enjoyed the music and story. The second StarTropics had graphics that blew my mind, everything just looked so smooth.