Super Mario World: 1-2 theme
Final Fantasy II: Main theme
Chrono Trigger: Magus' theme
WarCraft II: Human Campaign, level 1
Final Fantasy VI (III in US): Dancing Mad
I love a lot of the themes from FF6, but Dancing Mad enthralled me. When Nobuo Uematsu's band remade the 8-bit version I was giddy. I'm not really a "music guy", and outside of Uematsu I couldn't name another video game composer, but there's so much going on in Dancing Mad, it's like an entire story in and of itself.