Oh hey, neat topic. Let's go with a wide array of songs here.
Solstice: Title - Guitar Rearrangement by Tony Dickinson: Kastle Rock
Doom: At Doom's Gate - Dark Side of Phobos: Hangarmaggeddon
Streets of Rage 3: Moon - Streets of Rage Remake: Moon
Xenogears: Bonds of Sea And Fire - Xenogears MYTH: Bonds of Sea and Flames
Halo: Reach: In Amber Clad - Halo: Reach: We Remember
If We Remember doesn't qualify, I can put another one up in its place.
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Twostuck, Homestuck RPG: http://www.gamefaqs.com/boards/8-gamefaqs-contests/62168402