mp3Gain

==> http://mp3gain.sourceforge.net/index.php

What does MP3Gain do?

MP3Gain automatically adjusts mp3s so that they all have the same volume

You mean MP3Gain normalizes mp3 files?

Yes, but MP3Gain does not use "peak amplitude" normalization as many "normalizers" do. Audio files with very different peak amplitudes can still sound to the human ear as though they're the same volume.
Instead, MP3Gain uses David Robinson's Replay Gain algorithm to calculate how loud the file actually sounds to a human's ears.

To hear the difference between "maximizing" (peak normalization) and Replay Gain volume normalization,

1. Download this sample file
2. Unzip the two mp3 files, noting their current maximum amplitudes as indicated in the filenames
3. Open MP3Gain
4. Go to "Options -> Advanced..." and make sure the "Enable Maximizing features" option is checked
5. Set the "Target Normal Volume" to 92.0 dB
6. Click "Add Files," and add the two unzipped mp3 files
7. Do Track Analysis on the two files. Note that their volumes are only 0.1 dB apart
8. Without closing MP3Gain, listen to the mp3 files using your favorite mp3 player. Note how they're approximately the same listening volume
9. Now in MP3Gain, do "Modify Gain -> Apply Max Noclip Gain" (or press Ctrl-X). The two files are now peak normalized.
10. Listen to the mp3 files again. Even though their maximum amplitudes are now almost exactly the same, song clip 2 now sounds much too loud.

Does normalizing the mp3 degrade its quality?

No. MP3Gain does not decode and re-encode the mp3 to change its volume. You can change the volume as many times as you want, and the mp3 will sound just as good (or just as bad!) as it did before you started.