The Computability Menagerie houses animals of varying degrees of non-computability. The project started during my Marie Curie fellowship in Heidelberg, where I was working on a huge diagram of downward closed classes of Turing degrees, using JFig.
Mushfeq Khan and Joe Miller have written a web app version of the menagerie.
Related research on André Nies’ home page:
Tamer (computable) creatures are on display at the Complexity Zoo.