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Malbolge by Ben Olmstead

Dubbed "Programming from Hell" and specially designed with the view that programming should be hard.  It has seven instructions, and the program must be encoded in a rather random way.  It has not been proven Turing complete, and considering the automatic self-modification there is a good chance that it isn't.  Indeed it is so difficult to program Malbolge that it took someone ages to finally write a "Hello, world" program.

Muriel by Matthew Westcott

Monumentally Useless Re-Iterative Execution Language.  A language whose only means of control flow is to generate a new Muriel program as a string and then run it, without carrying forward the variables or returning to the original program.  Creating a loop in Muriel is like writing a quine.