There seems to be a considerable amount of interest in, and confusion about, the copyright law consequences of embedding a YouTube video in your blog. In fact, the Blog Herald just ran a story suggesting that bloggers could be on the hook for copyright infringement if they embed a video that turns out to be infringing.
Well, the news really isn't that dire. In fact, I'd say bloggers are generally pretty safe on this score, at least until someone notifies them that an embedded video is infringing.
First, it's important to understand what an embedded YouTube video is -- it's a link. Just a link. Nothing but a link. In fact, here's the entire html code needed to embed EFF's Corruptibles video into a blog:
<object width="425" height="350"><param name="movie" value="https://www.youtube.com/v/8-5INcUuoEs"></param><param name="wmode" value="transparent"></param><embed src="https://www.youtube.com/v/8-5INcUuoEs" type="application/x-shockwave-flash" wmode="transparent" width="425" height="350"></embed></object>
Taking a look at the actual code makes one thing obvious: no copy of the YouTube video is being stored on your server (only the HTML code for the embed). The video stays on, and is streamed from, YouTube's servers.
That makes the embedded YouTube video essentially indistinguishable from the in-line image links that are used all over the Web, including in Google's Image Search. In the recent Perfect 10 v. Amazon ruling, the Ninth Circuit made it very clear that where in-line links are concerned, there is absolutely no direct copyright infringement liability. So, for purposes of direct infringement, the answer to one question will generally resolve the issue: where is the copy hosted?
That leaves contributory infringement. If you link to a video that you know is infringing, or that any reasonable person would have known is infringing, and if your link materially contributes to the infringement, then you could be liable for contributory infringement -- a kind of "aiding and abetting" liability.
The contributory infringement test should leave plenty of breathing room for most bloggers. Two rules of thumb should avoid most issues -- (1) don't embed videos that are obviously infringing, and (2) consider removing embedded videos once you've been notified by a copyright owner that they are infringing.
If you want even more protection, you can register yourself as the "Copyright Agent" for your blog (requires a form and $80 payment to the U.S. Copyright Office), familiarize yourself with the requirements of the DMCA's online service provider "safe harbors" (the chief one for most bloggers will be notice-and-takedown), and take advantage of the same protections that shield Yahoo! and Google when they link to sites that may include infringing materials.
In short, embedding YouTube videos isn't that scary from a copyright POV, at least until a copyright owner takes the trouble to notify you.