The Pokemon, Legend of Zelda and Animal Crossing series have great soundtracks. I really like Gerudo's Valley from Ocarina of Time and Zelda's Lullaby.
I love the Sonic Adventure 2 soundtrack, I have a soft spot for Fly In The Freedom. Final Fantasy X & X-2's music is lovely, as well as Mario Galaxy - I got the double disc from Club Nintendo. Some music from Pok?mon Black and White are favourites of mine, particularly Lostlorn Forest's theme.
Animal crossing hour music from the original game, I think the nightime music is the most calming and mystical. Lost woods or sarias song, I love this song so much its probably my most favorite songs mostly from nastalgia, and I love the sacred grotto remix of the song. Super mario galaxy theme, ocarina of time theme, and fairys fountain theme from zelda. I will post more soon.
Mostly anything from Paper Mario N64.
Most notably, this beautiful, glorious song. Listening to it now gives me an amazing amount of feels. It sounds so hopeless, yet there's a touch of light in it. I don't really know. It's wonderful.
I'm rather fond of the songs for Pokemon Saphire, though, also.
Edit: I am pretty ashamed I forgot this. Usually anything to do with stars in game was also VERY beautiful.
This has to be one of my favourites. Unfortunately, people can't enjoy it as much without knowing it's context, but it's still so, so great. It always reminds me of the exact moment it plays during FF9.
I hadn't played the original Sonic the Hedgehog for about 6 years, so I kind of forgot. But Marble Hill zone has awesome music! I was surprised by how much I liked it.
I've not read through all the pages of this, so I apologize if this has all been said.
The end theme (setting sale, coming home) of Bastion is probably the single most amazing track, at least of what I can think of right now. It's just so perfect, and that along with the end is amazing.
Persona 4 had a great soundtrack, and the reincarnation version of the battle theme is amazing. The rest of the soundtrack is great too, but I don't want to link every one.
There's a few more that I think are pretty great like metal gear solid, FTL, Dark souls, super meat boy, but these are my favorites.