My two favorite math classes have been Number theory and abstract algebra.
Abstract was about all kinds of random math problems. That class was more about figuring stuff out than applying anything. One math problem we did was figure out how many configurations were possible in a 2x2x1 (not sure what the official name for it is, but it was Rubik's cuby)
Number Theory feels like a legitimate math class. It is all about proofs, but the proofs actually mean something. And the coolest part of the class is that our proofs build on earlier proofs. So it feels like we are making progressions into math.
It's also neat because it is all about familiar objects like 1,2,3, etc.
Some of my other classes that should have been cool, felt like they got bogged down into abstract details or they were all about applying the same things over and over.