So Twitter is everywhere these days. But it can be useful to build quick and dirty intranets, or set up real-time status updates without having to maintain an Instant Messaging desktop client running in the background.
There are a number of Web-based services that have used the Twitter real-time microblogging model to some success, and I will point you to a chart that I have with more details about each product here on my site.
They certainly are catching on. Both IBM and Oracle have developed their own Twitter-like application for internal uses, called BlueTwit and OraTweet respectively. With these services, there is little or no learning curve, they ensure that any messages aren't seen by the public or searchable by Google, and in general take the Twitter experience to a more secured enterprise collaborative level. And they are quick to setup and mostly inexpensive (in some cases a limited free version is available).
What are things to look for in your evaluation? Do you need software that runs behind your firewall, or can you use their hosted service and set up a private group that is only accessible for your employees? Do they integrate with your existing LDAP or Active Directory services so you don't have to create an entire series of user logins from scratch? Do you need file sharing integrated into the product, so your users can access a common repository of saved documents from within the discussions themselves? Do they work with mobile phone users and stripped-down browsers adequately? And what is the ultimate cost per user when you want to deploy the application?
Take a look at some of these products, and if you want a deeper dive Laura Fitton's Enterprise Micro Sharing Tools Comparison is a great place to start, even though it is about a year old.