It is my understanding that Spotify is (or at least was, when I saw their presentation), pretty much a Giant Twisted App with some C++ for parts that were too slow.
Lucasfilm, justin.tv, Launchpad and TweetDeck are some of the larger names you may have heard of. A bunch of smaller startups do too.
If you've been doing XMPP you've probably used a Twisted server (it's either that or ejabberd, mostly) at some point.
If you want Tornado, why not use Cyclone? It's a port (to Twisted) of Tornado; you get to write webby parts just like tornado's and you get the benefit of all of Twisted when you need it.
FWIW, I did the Twisted Help Desk and co-hosted the Twisted tutorial two years in a row now at EuroPython, and two years in a row that tutorial has had to move to a bigger room. Asking around showed a large portion of people were there because there place of work was either using or considering using Twisted. I never cease to be surprised by the stories I hear of people using Twisted to great success for pretty nifty applications.