I recently purchased a Zoom H2 recorder to use to record live audio (unamplified concerts, rehearsals, and other events) for the music academy at our church.  I purchased it because it’s simple enough for volunteers to use, and doesn’t require any extra software.  I’ve been very pleased with it.  It can record directly to MP3 or WAV.  It contains a microphone, and also has an input if you want to use another mic.  It would also be good for serious music students who want to record themselves and couldn’t already do it through a computer.  It’s $200, so it’s not for everybody, but it’s a great, simple solution for certain situations.