The BBC website needs no introduction, but I mention it here because I agree with Charlie Brooker that it is a 'national treasure'.
It is perfectly balanced, with an intuitive layout of information. The hierarchy doesn't at first glance seem as if it would be optimal, but when you use it, it just works. Everything is where you first expect to find it, and nothing you're searching for is hard to get at.
The design is classy and appropriately clear, with nothing unnecessary cluttering up the pages.
Other tangential applications are just as usable and smooth, and everything comes together as a unified whole.
We all use it and see it so often we don't really think about it, but it's many features are a swiss army knife with tools that will appeal to everybody, presented so well as for the whole site to be perfectly pitched for internet addicts, or new users.