YouTube includes a new section for "My Videos": a list of purchased videos. A YouTube help page has more details about the new feature:
You have the option of downloading and storing your favorite Partner videos and watching these videos even without an internet connection. To download Partner video:

1. Find the video you'd like to download.
2. Below the video's play bar in the lower left hand corner, you'll see a 'Download' button.
3. Click the 'Download' button to indicate that you'd like to download the video.
More at; http://googlesystem.blogspot.com/2009/02/buy-videos-from-youtube.html