The following links are purely FYI. When it comes to mp3s, we've adopted a "don't ask, don't tell" policy around here. (End of disclaimer).
But if you're interested...
Free Sound Recorder lets you record anything that is coming through your computer speakers (streaming media, for example) and save it as a sound file type of your choosing. The free download has 75% of the functionality of the one that costs money. You can find it here:
Replay Media Catcher does the same thing but for video. You can also separate out the audio and save it as an mp3. You can find it here:
So if there's a YouTube video of someone singing, say, "Come Thou Fount of Ev'ry Blessing" and you know you can't buy it anywhere, why, you can make a backup copy.
Our local library systems have a digital catalog where you can find audio books and music files (and even some kind of weird videos). Yours probably does, too, and it should be remotely accessible. Go crazy!