Structurally, the Adapter pattern is a class that implements an interface by (a small transformation and) delegating to another class.
However, this class structure is useful for more than just connecting two slightly-incompatible interfaces together.

A pipeline of adapters is sometimes an excellent way of decomposing a computation. 
For example, it is a reasonable design for a compiler.

This pattern is good for testability. 
In unit tests, one can test each section of the pipeline individually. 
In debugging integration problems, one can listen at any boundary by writing a decorator for that boundary's interface.
If some of the interfaces are the same, it may allow arranging the sections of the pipeline in a different order.