More or less traditionally referred to in conjunction with Twitter sources. At the first hand it is location based services. Although fewer than 1 percent of tweets are "geotagged," or voluntarily labeled by users with location coordinates. The second big area is natural language processing for tweets. For example, there are various demographics data that could be extracted and making sense of breaking news.
We would like to point attention to our old idea - Twitter as a transport. The system could be used as a transport layer. Think for example about many services that provide request/response cycles over SMS. Why do not use Twitter for this? Request data (and/or service) over Twitter rather than SMS.
For example, try to send the following tweet:
@t411 t GOOG
It will return to you (as a reply in Twitter) stock quotes for GOOG. Here:
@t411 is service address (a-la service number in SMS world)
t - is a request
GOOG is a parameter
Obviously, that such service could be a part of Twitter's offering. E.g. allow unlimited statuses for a fee, etc. It is Twitter for business.