If you don't mind about having a little work, i'd suggest this:
Step 1: Some sites are specialized on extracting music from roms and making them as a single file. Download those files. Some of them are .nsf (NES) and .GYM (Genesis).
The WinAmp (yeah, i'm old and i still like WinAmp) have plugins that support the playback of some of those files. Install them.
Ok, now you can listen to the original soundtracks as they were playing on the original consoles.
Step 2: Get into the WinAmp options and set the audio out as .WAV. That way WinAmp will open those .nsf or .gym (or any other plugin you might have installed) and record .wav files with each song.
.wav files extracted, all you have to do now is convert them into mp3.
I did this in some Sega Mega Drive files i had (such as DecapAttack soundtrack, i love it) and it worked perfectly.
But that was a long time ago. I assume there are easier ways to do that nowadays.
Here you can find a few players and files.
http://www.emuparadise.me/music/ But i don't know if they can extract into .wav or .mp3
HarvestDude™