I've been using Chatter since we pushed in live in our own org early this year. It's transformed the way I work and has become an indispensable tool. I use it to communicate with colleagues around the world, to talk about Force.com Labs apps, recruit developers and solve problems.
Note #1: These are generally EE+ Apps. However, Combo Pack, at the bottom, is PE+.
Note #2: Each of these has great video on their listing — click through to take a look.
Chatter Adoption Dashboard – This is a great way to see who is chattering about what in your org. It shows the number of posts, who has followers, most active posters during the last 30 days and more.
Chatter RSS – This "Chatter In" style of app let's you configure an RSS feed for your users. Once configured, Chatter RSS automatically fetches new articles on a regular basis. Users who have subscribed to a particular feed see them in their stream. If they want to stop seeing them, they simply unfollow. Watch the video on this for a detailed explanation.
Chatter News -This app also brings data into your org but it handles the problem in a slightly different way. With Chatter News, you subscribe to news feeds from Google Alerts on an account by account basis. News items are posted to the account's feed as they are received. As the admin, you have control over blacklisting news sources, the number of records to keep and more.
Chatter Invites – A key challenge for complex orgs is ensure people are following the records they should be. Chatter Invites is a great way to to tackle this. You can select any kind of record — a person, an Account, a custom object — and then find a number of people to invite as followers. Perhaps you have a key account or some other interesting data you would like some help with. Quick and easy.
Chatter Combo Pack – The Combo Pack has been around since the first release of Chatter. It's a great extension that actually includes 9 separate apps. The screen shot below is of Chatter Connector, an alternative way to visualize people in your org to see who you might want to follow. The Chatter Combo Pack is also available as a PE compatible app.
This is a small list. There are more than 20 Chatter related apps from Force.com Labs available. Take a look and try one today.