While not directly Nintendo-related, this collection of music is still pretty amazing. Chiptune artists use classic hardware to create music like you would hear on an old Game Boy, NES or64. The same sounds that created the original Super Mario Bros. theme or the Mega Man soundtrack are used to craft original works. While many of these songs are mediocre, I feel this collection stands far above the rest.
Japanese netlabel 16 Dimensional Records has released two albums of said songs: Gone Square and Go Square. The free albums have nearly 30 tracks of electronica-turned-chiptunes content that sound as if they came from a long lost NES game. Two of the early songs, Gerbera and Poinsettia, are some of the most impressive, so be sure to at least grab those if not the entire collection.