The following article outlines some common use cases one may encounter while developing RESTful web services using Dropwizard. It is entirely based upon the previous post on this matter, so it's advised that you go through it first and check out included source code package.
Articles on JAX-RS
Update 12/2017: While I think Dropwizard is overall a nice project I don't see benefit of using it over i.e. Spring Boot. Lean? Focused? Yes, until you reach the point when you need to actually do stuff and start adding to it. In that regard Spring is more complete solution and offers standard way to do these things.
Considering developing RESTful web services there are many options available for Java. To name a few one may consider Spring, writing them for a Java EE container with JAX-RS or even using something like Play Framework. Most of these are (heavier or thinner) integrated solutions though. When you step into one of these you buy it with the whole inventory of things they come with, not neccesserily targeted into developing RESTful web services.
Another approach would be to collect just what is needed to write such a service and glue them together in the project. The downside is, it takes usually some boring code to write integrating all of it into working solution (bootstraping, handling configuration files, etc.). And that is the reason I find Dropwizard helpful - it's more or less a collection of software for writing RESTful web services (Jetty, Jersey, Jackson), that takes boring stuff away and permits to jump ahead into writing the service.