String theory would be a good example. It is, in fact, not a theory. It makes no testable prediction. It's a neat bit of math and who knows, might even be correct. However at this time all it is is a neat bit of math, a hypothesis on how things might work. It won't even be a theory until they figure out how to make some testable predictions and won't be at all something to hang your hat on until there've been some serious tests of those predictions.
Actually, string theory may not be so immune to experimental feedback. The LHC offers both the possibility of providing experimental evidence (via the generation of supersymmetric particles), or of ruling it out all together if the decay rate of micro-black holes into neutrinos point to say 11 spacial dimensions, which is more than string theory can account for.
I must have slipped a disk -- my pack hurts!