YouTube lacks a lot of useful features that are available in other online video sites: a way to download videos, feeds for a user's favorite videos or for the comments of a video. So you can't download your favorite videos, or at least not directly from YouTube.
First you need a feed for your favorite videos and you can obtain one from
this site, which uses YouTube's API. Unfortunately, the feed only includes the most recent 10 videos.
To download all the videos from your feed, you can use
Miro, an open-source and cross-platform video player formerly known as Democracy Player. After you install Miro, go to Channels > Add Channel and enter the feed. Make sure you select "auto download all" and set the expire interval to "never" in the settings.

You can also download the recent videos from a playlist in a similar way. Although this is not a great solution if you already have a lot of bookmarked videos, at least you can automatically download all the videos you'll add to favorites from now on.
The format of the videos is FLV and you can play them using Miro,
VLC and other players or
convert them to other formats.
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