How to Convert MP4 to MP3

Use ffmpeg:

ffmpeg -i input_file.mp4 -vn -b:a 128k -c:a libmp3lame output_file.mp3

(Don't forget to adjust the audio bitrate, -b:a, otherwise you might get a huge file even for a low quality source.)

Many digital players actually support AAC audio as well, so you can try extracting the original AAC audio stream, without having to reduce quality even more:

ffmpeg -i input_file.mp4 -vn -c:a copy output_file.m4a

For older versions of ffmpeg, you'll need to use -ab & -acodec options instead of -b:a & -c:a.

With FFmpeg, which you can download as a static build (no installation needed) for every major OS:

ffmpeg -i input.mp4 -c:a copy -vn -sn output.m4a

vn and sn disable video and subtitle streams, if there are any. -c:a copy tells it to copy the audio bitstream as-is, without re-encoding the file. This will take less than a few seconds.