Oh boy...where to start
Super Mario Bros 1:
Everyone loves the default level theme :)
Underground Theme
Mario Kart 64:
Kalimari Desert
The Raceway themes
Start screen
But, my favorite one is the Starman theme. Really. In fact, it's my favorite composition of the starman in any Mario game. Period. I just wish there was some place to download it. ha.
Super Mario RPG:
Smithy Part 1 Theme
Smithy Part 2 Theme
Culex Theme (duh!)
Default Boss Battle Theme
Seaside Town
Booster Tower
Eh, they're just a few. Maybe in a later post I'll add a bit more.