Credited as the music producer of Minecraft, he is responsible for the aforementioned music, the ambient tracks used underground, the music included on the collectable in-game music discs as well as all of the sound effects.
C418 has released a complete soundtrack including 15 minutes of exclusive music not (yet?) featured in the game as well as “Cats” in stereo. You can purchase the original OST for $3.99 through bandcamp here
If you would rather use a big-name brand, you can also get the album via iTunes, Amazon and Spotify. However, it’s more expensive to buy via these services. You can now sign up for an “open” account at Spotify here in the UK and you can listen to the album for free! The audio is streamed in Ogg Vorbis at ~160 kbps, although you do get visual and audio adverts. Not too shabby :)