What is the SEO benefit of embedding YouTube videos on a page?

[ProjectLabs]

Is there SEO benefit to embedding YouTube videos made my other people or companies on pages?

The indirect benefit would be a better user experience and increased perceived value and usefulness of the page which could lead to more links.

Are there any other benefits?

[ProjectLabs]

Thanks everyone for all the great information!

[PhilNottingham]

Yes, there are lots of benefits.

Outside of the ones mentioned, you can get rich snippet results in the video SERPs (though this is rare) and you can also get "as seen on" attribution, which is a link at the bottom of a YouTube video that links to a curated page on youtube.com where it lists through a number of the YouTube videos featured on that site/blog, pulling in supporting text from the site. these curated pages provide a referring link back to the sites (through a 303 redirect). If you want to get this attribution, i would generally recommend only embedding one YT video on each page.

[SEOExecutive20]

Adding to All Star's point, bounce-rate has been debated  of  it's relevancy to SERP within Google. That is enough for me to consider it as a ranking factor.  Dr. Pete posted an article on this with some proof that Google is factoring in dwell time as a quality signal. Here is the URL to that article http://www.seomoz.org/blog/the-2-user-metrics-that-matter-for-seo

[Allstar]

To add to EGOL's good point, I'd add a viewing can be considered a "microconversion." The metrics you might positively affect are time on site, and if it opens in a shadowbox, potentially lower bounce rate.

[EGOL]

I believe that it produces a page with rich media that search engines might rank better.  And if it increases visitor engagement then that might improve your rankings through their links, likes, etc.

I add videos to a lot of pages.