"This video is no longer available due to a copyright claim by XYZ Inc." - That's the message you see on Youtube.com when they remove a copyrighted video clip from the Youtube website.
Sometimes the video is unavailable when the owner himself removed the video but it's still showing up in the video search results. Youtube will also delete videos that are porn or NSFW.
It is however possible to watch deleted videos on Youtube - Just like Google Cache stores a copy of a webpage on Google servers, Youtube may maintain a copy of raw video on their servers even when the video has been taken off the main website.
To retrieve this "deleted video", just supply the Youtube video id (available in the video URL) to Youtube Infamousx, and this service may retrieve the deleted video from Youtube for you. [via GHacks.net]
This trick will not work for videos that have been permanently deleted from the Youtube servers.