YouTube unofficially allows you to embed their “HD” quality videos on your site. All you have to do is append a line of text to the embed code.

To embed the “high quality” version of a YouTube video replace this:
https://youtube.com/watch?v=UNIQUE-VIDEO-ID
with this: (in the embed code)
http://www.youtube.com/v/UNIQUE-VIDEO-ID&ap=%2526fmt%3D18

To embed the “HD” quality version of a YouTube video replace this:
https://youtube.com/watch?v=UNIQUE-VIDEO-ID
with this: (in the embed code)
http://www.youtube.com/v/UNIQUE-VIDEO-ID&ap=%2526fmt%3D22

You can use this for linking as well:

• “Normal” YouTube link:

http://www.youtube.com/watch?v=iGpIT2bVZDw
(mono, resolution: 320×180)

• “High Quality” YouTube link:

http://www.youtube.com/watch?v=iGpIT2bVZDw&fmt=18
(stereo, resolution: 480×270)

• “HD” link:

http://www.youtube.com/watch?v=iGpIT2bVZDw&fmt=22
(stereo, resolution: 1280×720)

Keep in mind not all videos are available in YouTube’s “HD” format because they weren’t uploaded at high resolution… Here is an example of the three different quality levels:

Normal Quality:

High Quality:

“HD” Quality: