There's lots of places on the web to place free MP3's (all the yahoo type sites) but you'll have to trade off a lot of convenience. Most likely you won't be able to directly link to your files... which means anybody wanting to hear your music will have to surf through several pop-ups, advertisements and other pages until they actually get to your song.
Guys like me with cable hook ups want a direct link to the actual song so that it'll start playing immediately...within a couple of seconds.
If somebody posts an html website address here or a link to yet another link, I'll usually just pass on it cause it's too time consuming and frustrating to get the file working.
Another drawback is they'll only allow a certain number of people to listen to your songs before they cut you off for the day.
Yet another drawback is there's no guarantee that your file is going to stay on their server. One day your song just isn't there anymore and everybody's getting 404 errors while you think everything's still working.

For next to nothing you can get your own domain name, 500MB of space and the ability for people to download 500GB of your songs. You can post a direct link to your songs like this...

http://s93744050.onlinehome.us/mp3/MoogBoog.mp3

... and I can guarantee that about 99.9% of the time, with a cable hook up, you can be listening to the song in less than 5 seconds.

Another advantage of paying for your own server space is getting your own domain name and email addresses, setting up an online store, tracking downloads etc etc..

Some places like this one...
http://www.1and1.com/?k_id=6828651
...require a credit card in case too many people download your stuff then they start charging you $1.00 for every gigabyte over your limit.

Other places will allow you to pay by money order and give you 100MB space for about $30 or less per year.

Hell, for $30 a year, just get a paper route or or take some stuff to a pawn shop or something.