I'll just put down my own list here.
- The Touhou series, all by ZUN (and all on PC, pretty self explanatory here)
- Cave Story (PC)
- VVVVVV (PC)
- The Megaman series on the PS1 (not the older consoles)
- Grandia III (PS2) - The first battle theme is my personal favorite. Some of the other tracks are okay and some seem repetitive.
- Pokémon 1st Gen games (R/B/Y, all on GB)
- Pokémon Mystery Dungeon Red/Blue Rescue Team (GBA/DS). The ones that has the 4th Gen Pokémon (Time/Darkness/Sky) has a more eerie atmosphere.
- Fast-paced music-rhythm game music like IIDX, DJMax, O2Jam (erm, my avatar), and DDR. Although I have to admit that I only like about half of the songs in the DJMax franchise.
- BMS of Fighters series
There's probably more I like but I'll just stop it right here for now.