Well, you have wormholes (but they require exotic matter) and anything with singularities in it; there is the Gödel solution of a "rotating Universe" (which could be true for a "parallel" universe), the van Stockum's solution and so on. I guess until closed time-like curves are proven to be unphysical (which seems likely), physicists will keep coming up with possible solutions to Einstein's equations which allow for CTCs (and refuting them). And who knows, maybe one of them can be implemented by humans.

On the other hand, it would be very interesting to know what is the mechanism by which the Universe protects itself against CTCs.