If you run a website, like many of our readers, and you have an account system, you probably have problems with spam. One of the main sources of spam is users who register using disposable e-mail addresses. These can be generated by spammers programatically, using services like the Guerilla Mail API I covered previously, and used to make tons of accounts to try to get blog spam through. If this is a problem for you, the DEA Filter API can help.
The many developers who use the Twitter API have built thousands of creative applications that have certainly exceeded anything that Twitter's founders could have initially imagined when the API was released (for examples of some of these applications, check out our growing list of hundreds of mashups that use the Twitter API).