Static nested class in Java, why?

The Sun page you link to has some key differences between the two:

A nested class is a member of its enclosing class. Non-static nested classes (inner classes) have access to other members of the enclosing class, even if they are declared private. Static nested classes do not have access to other members of the enclosing class.
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Note: A static nested class interacts with the instance members of its outer class (and other classes) just like any other top-level class. In effect, a static nested class is behaviorally a top-level class that has been nested in another top-level class for packaging convenience.

There is no need for LinkedList.Entry to be top-level class as it is only used by LinkedList (there are some other interfaces that also have static nested classes named Entry, such as Map.Entry - same concept). And since it does not need access to LinkedList's members, it makes sense for it to be static - it's a much cleaner approach.

As Jon Skeet points out, I think it is a better idea if you are using a nested class is to start off with it being static, and then decide if it really needs to be non-static based on your usage.

To my mind, the question ought to be the other way round whenever you see an inner class - does it really need to be an inner class, with the extra complexity and the implicit (rather than explicit and clearer, IMO) reference to an instance of the containing class?

Mind you, I'm biased as a C# fan - C# doesn't have the equivalent of inner classes, although it does have nested types. I can't say I've missed inner classes yet :)

There are non-obvious memory retention issues to take into account here. Since a non-static inner class maintains an implicit reference to it's 'outer' class, if an instance of the inner class is strongly referenced, then the outer instance is strongly referenced too. This can lead to some head-scratching when the outer class is not garbage collected, even though it appears that nothing references it.