I recently found out that you can link directly to a specific time in a YouTube video. All you have to do is add a #t= anchor to the end of the URL that indicates the time position in minutes and seconds. Here's an example that links to the video for Cage the Elephant's "Ain't No Rest for the Wicked:"
http://www.youtube.com/watch?v=5t99bpilCKw#t=00m08s
The #t=00m08s anchor causes the video to begin playing zero minutes and eight seconds after the beginning. There's also a way to accomplish the same thing when embedding a video. Add a start parameter to the video's embedded URL in both the embed and param tags. The value of start should be the number of seconds to skip before playback.
Here's an example that skips the first 20 seconds of formal Congressional banter -- for what purpose does the gentleman from Ohio arise? I reserve the right to revise and extend my remarks! -- before U.S. Rep. Dennis Kucinich's recent speech about TARP funds. The start parameter is in bold:
<object width="480" height="385">
<param name="movie" value="http://www.youtube-nocookie.com/v/cq5fT6bhCrE&hl=en&fs=1&rel=0&start=21"></param>
<param name="allowFullScreen" value="true"></param>
<param name="allowscriptaccess" value="always"></param>
<embed src="http://www.youtube-nocookie.com/v/cq5fT6bhCrE&hl=en&fs=1&rel=0&start=21" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="480" height="385"></embed>
</object>
This HTML markup starts the Kucinich video 20 seconds in when a viewer chooses to play it.