The most obvious well designed website that comes to mind is Google. It’s the most popular as well. For anyone that has been living under a rock, it is the best search engine. When searching, the most visited or efficient link is usually at the top of the search index. It’s extremely simple to use. Filtering options are available as well to narrow a search, it is very efficient and simplistic.
Another well designed website that I personally like is YouTube. It filters usually by viewing, but that can be changed due to preference. What I like about YouTube is that the layout hasn’t changed too much over the years (like Facebook). Similar to Google, I appreciate the simplicity. They have the video on the left with related videos on the right. It’s also easy to explore, I find myself getting caught surfing from video to video, at one point I’ll be watching a tutorial and the next I’ll be watching soldiers coming home to their pets.