Popular Nonmusic Websites
Any website at all can post an MP3 file. It does not have to be a music site. In fact, sometimes being posted on a non-music site can make you stand out.
Beatnik Turtle has had good luck with this idea. Once, Beatnik Turtle wrote a song about a boardgame by a small but popular game company. We ended up sending it to the president of the company and he asked us if he could post a link to the song on his website. We ended up getting thousands of downloads out of that. In fact, over a year and a half later, we still get hundreds of downloads of the song a month. It has been posted to blogs and mentioned on other unrelated websites since then.
The song was titled "Were All These Beer Cans Here Last Night." The reason the song got so far is that the games site had a high search rank due to its popularity. When our song was on their first page of news, it was near the top of a Google search for "Beer Cans." Posting it on the front of our own website would not have gotten the song as far, but getting it posted to another site with heavy traffic helped a lot.
If you try to do something like this, we suggest just giving them a link to your song, not the song itself. If you just send them a link, your website statistics will show how many times the song was downloaded and you will have control over it. While it does give you control about taking it down, the most important thing is that you have control about leaving it up. Since we still get hundreds of hits per month for the song (in the last four months, there were 1900 downloads of the song,) we want to leave it up forever if we can.
Another site that we had luck with was the site No Pants Day (nopantsday.com). They searched the Internet for links related to No Pants Day, and found the Beatnik Turtle song "I've No Pants." We happily let them post it to their site, as Beatnik Turtle is, in fact, pro-no pants. And we vote.
If you see a site that you enjoy, check if you have a song that might suit them or see if you feel like writing a song for it. Some of these websites would be flattered to have a song written about them and are happy to post music. The main reason this technique is so effective is that those websites are not promoting you, they are promoting themselves.