I am not really a remixer (I have done a few but none for games) BUT I have made 2 Diablo 3 themed songs... because I play the game and like it. After the completion of each song, I was able to get one of them promoted on a really popular fan site known as (DiabloFans.com) and the other was promoted by the gaming company Blizzard themselves (Battle.net), which was really awesome. There are a lot of good methods of sharing your original music or remixes but having them promoted by fan sites or the actual company themselves has proved to be the best way to share and receive exposure that I have experienced.
Based on what I have seen, I don't think many (Game fan sites and Gaming companies) receive much fan made music so I think most of them are more than happy to share it when a producer goes out of there way to make some.