What? Twitter can be a feature in my app? How can a web service like twitter be a function of my app?  If you look below the surface of twitter, it is a pure web service, and I mean service from an API perspective.  Lets keep that in mind as we explore this further.

So how can twitter the web service serve me in building my applications/sites/widgets? Well quite simply twitter gives us a truly portable social communications tool that is really, really flexible. Twitter should be seen as a support for your services to make them more portable and accessible.

So what do I mean by portable and accessible? Well first you need to cast away the notion that a website is only to be seen through one container (www.yourdomain.com for example). RSS, APIs, and a litany of other platforms should have changed your mind years ago.  Twitter gives you access to a number of things that are potentially useful for your endeavor:
Mobile Integration: A solid mobile platform (let them leverage the costs, last thing you need to do is pay $2k/month for an sms number + thousands in sms fees)
Jabber/IM Integration: Instant messaging based commands and controls (bots?)
Social Graph: A very flexible social graph and the ability to leverage relationships
Users: Roughly a million of them

The key to this is the ability to quickly and cheaply integrate mobile controls for your application, something no other platform is really offering at the moment.  Why not let your users post to and retrieve data from your site using their mobile phones? Why not let them interact with your application through instant messenger?  The possibilities are endless folks, you just have to look for them.