You can use Akka for several different kinds of things.
I was working on a website, where I migrated the technology stack to Scala and Akka. We used it for pretty much everything that happened on the website. Even though you might think a Chat example is bad, all are basically the same:
Especially the live updates are easy since they boil down to what a Chat example ist. The services part is another interesting topic because you can simply choose to use remote actors and even if your app is not clustered, you can deploy it to different machines with ease.
I am also using Akka for a PCB autorouter application with the idea of being able to scale from a laptop to a data center. The more power you give it, the better the result will be. This is extremely hard to implement if you try to use usual concurrency because Akka gives you also location transparency.
Currently as a free time project, I am building a web framework using only actors. Again the benefits are scalability from a single machine to an entire cluster of machines. Besides, using a message driven approach makes your software service oriented from the start. You have all those nice components, talking to each other but not necessarily knowing each other, living on the same machine, not even in the same data center.
And since Google Reader shut down I started with a RSS reader, using Akka of course. It is all about encapsulated services for me. As a conclusion: The actor model itself is what you should adopt first and Akka is a very reliable framework helping you to implement it with a lot of benefits you will receive along the way.