Audacity - Reviews and free downloads at Download.com. The most popular freeware MP3 and audio editor in general. The only issue is that while powerful, it edits in uncompressed WAV file and so recompressing is a hassle.
Ideally, an editor would keep the MP3 in its encoded form and edit from there. Saves time and won't introduce artifacts as you uncompress and recompress.
"Wavepad":http://www.download.com/WavePad/3000-2170_4-10382895.html. This is a simple mixing application. Let's you record then do format conversion. Kind of useful for making basic podcasts I think but I have to try it.