There are a lot of classics out there and I could be here all day giving you lists and lists of retro games with great music and sounds. But I would rather focus on a few newer titles that people may underrated or don't know about.
Bastion as mentioned above is one of my all time favorite games. And a big reason for that is the music and narration. The music blends and ties in with the game and atmosphere so well. It moves you, makes you feel something. It's a soundtrack I have specifically on my Spotify playlist and I listen to it religiously. If you haven't yet -- go play Bastion. And if you aren't interested in playing it, go find the soundtrack online, you won't regret it.
The other is a newer rogue-light title and that is Overture. It's a fun and light hearted game that you shouldn't take too seriously. What I love about it so much is that it's a real throwback to the old 16 bit titles, and the music is the same way. It's upbeat, it's catchy, and it's 16-bit! Are your serious? The game is only $4 on steam and I would say the soundtrack alone is worth it, even if you don't care for the game.