Hmm... If I had to narrow it down to just one, I'd say "Door ~ Kaze ga fuku HOSHI de ..." by Miki Takahashi from the video game Evolution Worlds. First off, it's a pretty song. Second off, it's the first Japanese pop song I ever heard, and that makes it special to me. Here's a link... Spoilers for that game, if you care.
Other songs I've really enjoyed are "To Zanarkand" from Final Fantasy X, "Warriors of Earth" (main theme) from Sakura Wars: So Long, My Love (it really gets me pumped up!), and the final boss theme for Sonic Colors (downright scary). And, speaking of Sonic, I like a lot of Crush 40's stuff (e.g. "It Doesn't Matter"), and a lot of the stuff from Sonic Heroes. I also loved the theme of sadness from Sonic Adventure 1.
The Super Mario Bros. theme song is always good. And I really like the boss music theme from Super Mario RPG. The ending theme to MK64 too. The Galaxy games just had awesome music all around.
The Advance Wars series had good music, though I can't pinpoint any certain song. The main theme and theme of sadness from Skies of Arcadia. I also like "Whisper of Hell" and the theme of sadness ("Sorrowful Angel") from Disgaea 1, and the opening themes for Disgaea 2 (cool) and Disgaea 3 (funny). The song that plays in Trauma Center: Under the Knife 2 when you're up against new forms of GUILT was super intense. Pokémon White/Black Version's Team Plasma theme was enjoyable. I really liked the trainer battle theme from Pokémon Ruby and Sapphire. Ashley's theme in Wario Ware: Touched! was quite amusing.
Whew, I think that's everything for me.