At my previous startup we used Scala with Unfiltered and Akka for processing lots of data from recipe sites and food stores (NLP stuff, scrapping, retrieving ingredients, matching ingredients with goods etc.), Play framework was also used for admin board and marketing backend.
I personally use Scala / Akka to learn about distributed programming, concurrency, compiler and DSL building etc.
Apache Spark is also written in scala. http://spark.apache.org
Scala is used for a lot for systems programming. I personally use the JVM for my distributed machine learning work.
I am currently building a web based database management tool in Scala and Backbone.js. Our initial prototype was built in Python, but Scala proved to be multiple times better fit for this kind of project.
Also we now offer both self-hosted and in cloud versions mainly thanks to JVM.