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gwern comments on Some Heuristics for Evaluating the Soundness of the Academic Mainstream in Unfamiliar Fields - Less Wrong
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I don't have any good examples of actual irrelevant/artistic mathematics, but possibly:
"Unipotent Schottky bundles on Riemann surfaces and complex tori" http://arxiv.org/abs/1102.3006
would be an example of how opaque to outsiders (and therefore potentially irrelevant) pure mathematics can get. I'm confident (primarily based on surface features) that this paper in particular isn't self-referential, but I have no clue where it would be applied (cryptography? string theory? really awesome computer graphics?).
There's one funny quote I like about partially uniform k-quandles that comes to mind. Somewhat more relevantly, there's also Von Neumann on the danger of losing concrete applications.