A few personal favorites:

Vimeo - Unquestionably the best-designed video site. It really helps to nurture the strong artsy/film community that makes Vimeo so special. http://www.vimeo.com

Hype Machine - not a web startup, per say, but I really like the format they use. Simple, clean, and easy to quickly listen to the hottest new stuff. http://hypem.com/

Grooveshark - much stronger than most music radio sites; I'm looking at you, Pandora! http://www.grooveshark.com

Twitter - great, compared to Facebook (and in its own right). I really like the clean and upbeat design flavor Twitter has. Twitter has to distill much more information in a newsfeed than Facebook and yet still manages to be more effective. http://www.twitter.com

Tumblr - obviously design is a strong part of Tumblr's culture and success. No question on it being one of the best-designed tech sites around. http://www.tumblr.com

Heroku - no experience using the service, but their home/about pages have that unique dark theme that works quite well. http://www.heroku.com