Being prone to nostalgia at times, I get that melancholy feeling from certain game songs. My five favorites?
Sega Saturn - Sonic R
This may sound like a weird choice. The game itself was only decent and not outstanding. The music, however, strikes a melancholy chord with me. This especially goes with the song "Livin' in the City." I can remember first hearing it when seeing a display of it in a Best Buy back in 1997. I think it was a Best Buy, anyway. I eventually got the game. I was, of course, 9 years old at the time. I still say it's one of the best soundtracks in a 3D Sonic game, even if that's not saying much.
Sega Saturn - NiGHTS: Into Dreams
What can I say? I still to this day find the music in this game to be beautiful, if a bit dated. Beautiful music for a beautiful game. Fitting, isn't it?
Capcom - Many Systems - Street Fighter series
Now, I'll be honest. I may be a bit biased here, being a fan of 2D fighters. But I absolute love the music in some of the Street Fighter games. Personal favorites are Super Street Fighter II: The New Challengers, Street Fighter III: 3rd Striker, Street Fighter Alpha 3 and Street Fighter Alpha 2.
Sega Genesis - Streets of Rage 2
Aw yeah. One of my favorite "club" soundtracks in a videogame. What can I say? Yuzo Koshiro's compositions can really help one get into this game more. It fits perfectly.
Nintendo Gamecube - Metroid Prime
Yes. Metroid Prime. The first one. I haven't played the other two, but from what I remember of the first, the music was wonderful. Its haunting ambience truly added a beauty to the environments, especially the snow area(sorry, forgot the actual name of it).