YouTube is using the HTML5 History API to add and remove page URLs to the history stack. This results in the URL changing in the address bar, and the back/forward buttons working, while still actually loading the page via JS (ajax).
The easiest way to implement the API with backwards compatibility at this point is by using History.js. By backwards compatibility I mean falling back to the hash tag method for older browsers that do not support the HTML5 History API yet.
Check out the History.js demo!
I think Twitter is probably the best known example of a website using hashed URLs. For example twitter.com/#!/username has been a common sight for years. The problem with this method is that hash tags are client side, thus you need JS to read them and serve the proper content. Any non-JS user clicking a hashed URL will just land on Twitter’s homepage.
Beatport was one of the first major websites using the HTML5 History technique by the way. SoundCloud has recently implemented it too. Both sites needed HTML5 History badly, to ensure audio playback while visitors browse through pages.