I think we've all played a game with limited hardware that did a suprising job or providing good music you loved to hear. So let's hear it. Which songs do you remember and which ones did you love? It doesn't neccesarily have to be a 16-bit or 8-bit game, my main point was to not cite games like Skyrim which can now afford to shell out for some rather respectable composers utilizing full orchestras of people, and instead stick to games where it's like they hired some nameless joe to do the composition on a budget and they excelled. For example Banjo-Kazooie comes to mind as a game where a big name wasn't called in to do the music with a full orchestra, and instead it's one guy fiddling around with a soundboard and it came out great. A lot of old N64 or PS games - or even some Gamecube/XBox/PS2 games - qualify for what I'm talking about, so don't be shy about naming games like that.
As for me?
For me that's easy:
https://www.youtube.com/watch?v=vQuK6nwq__E
https://www.youtube.com/watch?v=BrdN92L0IRs
https://www.youtube.com/watch?v=zxPRfIV4mXA
https://www.youtube.com/watch?v=wPxIkmaUoEU
And last but most importantly:
https://www.youtube.com/watch?v=uReaofy9ZQ4
That song clearly inspired the boss themes and I cannot tell you how much that singular little tune did so much and was so important for the tone of the game. Every level of Wario Land 4 involved fighting to the end of it, activating a bomb and then racing back to the start through newly spawned enemies, and every time it sparked that song. No song felt more fitting than that one when it came to adding the tone of "you better hurry the hell up." Here's just an example of what the gameplay would look like in case people are curious: http://youtu.be/QYjUn_vD66E?t=59m39s