In some of my projects and in some books was said to not use inner class (anonymous or not, static or not) - except in some restricted conditions, like
Anonymous inner classes has benefits in being able to see the fields and variables around the "new" statement. This can make for some very clean design and is a quite nice (but a bit wordy) approach to "how can we make a simple version of lambda statements".
Named inner classes has the benefit of having a name, hopefully telling, which can be documented in the usual way, but which is tied together to the surrounding class. A very nice example is the Builder pattern, where the inner class is responsible for providing state for the initialization process instead of having numerous constructors. Such builders cannot be reused between classes, so it makes perfect sense to have the Builder tied closely to the parent class.