Not sure if this is new or I'm just late to the game....but embedding YouTube and Vimeo videos into your Wordpress website is as simple as pasting the video's URL. I cannot attest to this working with any other services; but it definitely worked for these two.

I was filtering through a bunch of bloated video embedding plugins when I stumble across this post on the Wordpress.com support section. Basically it just says to paste the URL and Wordpress takes care of the rest.

Pretty slick.

So I decided to try it with a YouTube URL and lo an behold! It worked just the same!

Vimeo

Wordpress does have some shortcodes available for Vimeo which will allow you to adjust the size if needed:

[vimeo http://vimeo.com/240975 w=500&h=400]

YouTube

YouTube works too, but the format is a bit different:

[youtube=http://www.youtube.com/watch?v=JaNH56Vpg-A&w=320&h=240]

Do not show related videos afterwards:

[youtube=http://www.youtube.com/watch?v=JaNH56Vpg-A&rel=0]

See the support articles here: Vimeo - YouTube

All I can say is bravo Wordpress.