I meant some open source applications that are built in a distributed way (hence using something like AMQP in a publish/subscribe fashion)

I don't really know of any. Nobody writes these sort of distributed applications from scratch. They're almost always evolved from monolithic database-backed applications. And the process of evolution is half development half ops. I doubt that tumblr as it exists today could be deployed from scratch, even if you had all of the source code of all of the systems.

However, if you want to go truly distributed (much more so than any website I know of) there are open source projects you can learn from:

http://freenetproject.org/

http://amule.org (or http://mldonkey.sourceforge.net/Main_Page if you're into functional programming)

http://www.torproject.org (especially the hidden services stuff)

And you probably want to read this: http://pmg.csail.mit.edu/papers/osdi99.pdf