Did you know that you can define (even @Override) methods to enums pretty much in the same way as classes?
Instead of having the #accept(File) method checking on the “type” to decide on the operation, you can move the operation to the type itself! :D
Personally I believe the SuffixFilter is a bit of an overhead to implement with inheritance to just encapsule the
"^.*" + Pattern.quote( suffix ) + "$"
Maybe a Factory is more appropriate. Which can also be used to create other file filters as well.
The #all makes it easy to have your RegExFilter decoupled from the TypeFilter.
Try to avoid static Util classes as are harder to extend or test. Instead you can use composition to “extend” a File to add more methods
Also notice how the stop condition for the recursion is easier to identify.
Kudoz to @imperez for his Regex to find the first part of a url post and @cahnory followup comment.
Though it doesn’t apply to files, I did remember his post while looking at yours :)