There are so many, but the oldest one I can think of right now is Dearly Beloved. I'm going to post the BbS version though.
*Youtube video snipped*
The Kyle Landry version of that song is just great. Well, they're both great, just in different ways.
I listened to this osong on repeat for days after hearing it for the first time. No idea why, it just relaxes me.
No gaming music thread can ever be complete without anything from the Chrono series.
Special meaning to me because it's the first proper thing I ever learnt on the piano.
Some great choices, special nods to the wild arms song and duck tales theme.
I could post a few more wild arms one that meant a lot to me but will try and mention songs from games that haven't been mentioned yet.
You only hear this once in the early stages of FFIX, but does a lot to get you in the mood and prepare yourself for the rest of the game :) When reminded of FFIX, tis this song I think of first.
I feel I have to include one from Vagrant but am torn on picking just 1 song... Actually quite a few personally relevanvent songs but guess the dragon boss theme edges it out as being the most memorable and fits the mood perfectly (you're fighting a friggin dragon): Isn't anywhere near the best song of the game, but most memorable due to being associated to some great boss fights.
Remastered version of one of my oldest fav themes :) Golden Axe 2, fuck yeah.
Well there's this:
and this one too:
and finally this:
And those are just off of the top of my head!
I'd say any of the songs in Braid. Most games have the music added in later, but the artist for Braid actually designed the style of each level based on how the songs made him feel.
Memories of You from Persona 3 (aka the end credits song), which is unintelligible to me lyrics-wise but for which the emotion comes through perfectly. Also, the final credits song for Mass Effect 1
Not this version per say, all of them, It was the theme playing the first time a game really moved me, when i walked out onto that open field.
The Opera Scene from FF6. Nothing can replicate the "holy crap they're actually pulling this off in 16-bit!" chills I got the day I played through that scene.
From one Golden Sun fan to another; +5 internets and a free cookie!
Lights. The music to the last level in Lumines before it starts over. It was just such a soothing song to end a frantic last couple of levels.