Following functional style in Java can require some forethought due to the language's roots. However, its possible to identify certain patterns and rely on libraries to make functional programming easier in the Java language.
In a first post over at the cuberick blog, you can find a discussion on anonymous inner classes being a poor man's closure -- the latter term being a popular functional construct.
On a second post, you can hear Mario Fusco's podcat on the Lambdaj project, which is also aimed at functional stlye in Java and of which he is the creator.
Read the post 'Anonymous Inner Classes: A Poor Man's Closure?'
Hear Mario Fusco's podcast on the 'Lambdaj Project':