That framework is Spring MVC.
It is DI, adapters for vendor-specific libraries and utility. It's probably not the easiest thing to start with just because it is so flexible that it can be hard to know where to start. A good "Hello World" Spring MVC 3.1 app would go a long way.
I really would like to use the Play Framework and it's so close to being great but it just falls too far short.
I really liked Play 1.x with Groovy templates. It was simple and it pretty much just worked.
Play 2.x has gone in a radically different (and backwards incompatible) direction. It is now part of Typesafe and the goal of Play 2.x is to make Scala a first-class citizen.
The problem is that many of the niceties of Play are either harder to use or just outright missing in Java Play 2.x (eg AppEngine support and the OAuth client were all present in 1.x and are slated for a future 2.1 release).
There really is a niche for a Java Web framework that like Play ditches the JEE/servlet model in favour of the Rails/Django way of doing things (including dynamic class reloading) but doesn't do it in a way that makes me want to stab myself repeatedly.
This would include playing nice with the Java ecosystem (seriously just use Maven and to hell with SBT).