I usually only use statics in conjunction with the friend system.
For example, I have a class which uses a lot of (inlined) internal helper functions to calculate stuff, including operations on private data.
This, of course, increases the number of functions the class interface has.
To get rid of that, I declare a helper class in the original classes .cpp file (and thus unseen to the outside world), make it a friend of the original class, and then move the old helper functions into static (inline) member functions of the helper class, passing the old class per reference in addition to the old parameters.
This keeps the interface slim and doesn't require a big listing of free friend functions.
Inlining also works nicely, so I'm not completely against static.
(I avoid it as much as I can, but using it like this, I like to do.)