This is the (US) legal situation as I (a layman, not a copyright lawyer) understand it:

Most of the content on YouTube is pirated, despite their explicit policies against such practices--I'm sure that most posters have not sought the necessary permissions and licenses to use the performances they've recorded, the music tracks or images they include or the works they perform. Capturing video or audio from YouTube is also (in most cases) pirating.

However, a number of clips include public domain material, such as audio recordings now in the public domain or videos made by the government. Montages, even of public domain photos, might constitute copyrighted original creative works by the compositors, much like performers' arrangements of folk songs. I'm not sure whether simply packaging pd stuff as a clip constitutes "original work"--that seems pretty bogus.

"Fair use" policies might apply if you're capturing materials for personal study. Capturing for personal enjoyment would not qualify, so you might have a hard time in court proving "fair use".

The fact that you own a recording in one medium doesn't legally give you the right to pirate another copy from a separate source (like YouTube). But I think the law allows you to make a copy, for personal use only, from a recording you legally acquired. Once you start giving copies to friends, you've crossed the legal line.

While the capture advice in this thread will mostly be used to pirate or re-pirate material, it also applies to perfectly legal usage. Tape recorders were ostensibly sold so people could make recordings of themselves or of events they had full rights to record (and indeed, many did.) I believe the situation is the same with YouTube captures, though much less is legally capturable.

What would really help is if people adhered to the letter of the law. Then public outrage against current copyright restrictions would grow so heated, the various governments would be forced to revise the laws in favor of the people and rational use (for a change).