It is also used anytime you don't want anybody to be able to instantiate your class. Utility classes come to mind, like the Math class... all the useful methods are static, so you don't NEED to create an instance.
There are only two hard things in computer science: cache invalidation, naming things, and off-by-one errors
Another pattern where it's used is the Typesafe Enum pattern, where the only instances are static final fields inside the class itself.
The soul is dyed the color of its thoughts. Think only on those things that are in line with your principles and can bear the light of day. The content of your character is your choice. Day by day, what you do is who you become. Your integrity is your destiny - it is the light that guides your way. - Heraclitus