http://chartbeat.com/demo/#
https://indinero.com/dashboard?ajaxpopup=livedemo
among others...
How do they do it? I'm not a designer but I always wanted to know what's the web 2.0 "secret".
BR
The user interface exposed to the user would extensively use javascript to make the web pages interactive. By using Ajax, the webserver can send and receive data without making the user go to a whole new page (eg. clicking the upvote button on HN), this makes the webpage act more like a application. This can be done via javascript, which can send and recieve json/xml/html. You can use libraries such as jQuery, mooTools, YUI which allow you to more easily and cleanly implement these. You can also combine these with flash do even more nifty things (eg. graphs on google finances). As far as getting ajax stuff to work on the server side, all you need to do is have specific urls return json/xml documents instead of html.
As far as looks, it's all about the stereotypical pastel colors, rounded corners, gradients, minimalistic looks, beautiful typography, and usually accompanies with a 'beta' label no matter how early or finished the product is.
As far as server side, sites like these are also expected to have a API exposing the web page's functionality to the outside (eg. a desktop screensaver that uses flickr's photos).
Another aspect is making the so called web2.0 site also more connected to 'social' networks such as facebook/twitter. This can be done via the web APIs exposed by facebook/twitter on the client side, or you can connect those site's server APIs using your own web server.