You really have to take it on a case by case basis. The first question that you have to ask yourself is if the person making the complaint actually the owner of a copyright? Secondly, even if the person is the owner of the copyright, does the use constitute a 'fair' use? (Really all you can do is to look at the content itself to make that determination. Some content can be borderline of course, ie. is it newsworthy? constitute a parody, etc. etc.,) At some juncture, you also have to put some business sense into it as well, ie. is it worth it for me to bother with this, or is it simply easier to remove the content?

YouTube is a private entity, the first amendment does not apply as between the user and you tube.

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