How can I normalize the sound levels in several different audio/MP3 files?

Audacity

MP3Gain

MP3Gain does not just do peak normalization, as many normalizers do. Instead, it does some statistical analysis to determine how loud the file actually sounds to the human ear. Also, the changes MP3Gain makes are completely lossless. There is no quality lost in the change because the program adjusts the mp3 file directly, without decoding and re-encoding.

Though I think Audacity is more reknown

Audacity is great, but you might also want to check out Levelator.

Levelator adjusts the audio levels within your podcast or other audio file and it runs on Windows, Mac OS X, and Linux.

I hope this helps.

Audiograbber will normalize the volume level of audio. It does a nice job of it:

Audiograbber is a beautiful piece of software that grabs digital audio from cd's. Audiograbber can automatically normalize the music, delete silence from the start and/or end of tracks, and encode them to a variety of formats including MP3. Audiograbber can download and upload disc info from freedb, an Internet compact disc database. You can even record your vinyl LP's or cassette tapes with Audiograbber and make wav's or MP3's of them.

If a command line utility is ok, I'd definitely recommend normalize.

I especially appreciate the batch mode with which you can normalise an album while preserving the relative volume levels of the tracks.