Why is it common to see videos uploaded to public forums that contain copyrighted material (eg. Music) when it would appear that it is illegal?

is it ignorance, a 'safety in numbers' mindset, a lack of policing, or can you do it within the law?

In a nutshell

Apparently the owner can arrange to block itcompletely or allow it with conditions. Some of the conditions are that they get a cut of the revenue from the extra adds and popupspYouTube will place on the video. Everyone's still taking a cut in some way.

Apparent!y there are organisations that will monitor YouTube, Vimeo etc on your behalf as a copyright holder. They'll contact YouTube etc on your behalf if they find your work. This is in addition to the clever audio recognition in YouTube.

For some ownerso/ labels its probably better to have the material used as backing music - getting it out there

It's fun to see the techniques folks have used to try and prevent the auto recognition of commercial audio tracks