I just read through the RFS (http://ycombinator.com/rfs.html), which was written in 2009. I'm not sure if YC is still looking for those types of products. More specifically, there's an item that says "Things built on Twitter".
Recently every investor I talked to didn't like products that are built on top of Twitter, and I wonder if YC's perspective has also changed.
Twitter, and specifically the API team, has worked hard to come up with guidance for where they think there are opportunities in the ecosystem.
They have very clearly told third-party developers to stop making Twitter clients [1]. Twitter wants to own the display of tweets since they are focused on making advertising their core business.
But there are definitely opportunities if you think beyond just making clients. The five main categories that Twitter specifically mentions are: Analytics, Curation, Content, Publishing, and Enterprise [2].
To echo PG, there are definitely still big companies to be built on top of Twitter. You just have to think big to begin with.
[1] https://groups.google.com/forum/#!topic/twitter-development-...
[2] https://dev.twitter.com/blog/ecosystem-showcase