... what do you do?
Over the last five years or so there has been a test case for this in particle physics, where experimental results and the expectation from theory were completely at odds: qualitatively different, and (where they could be compared numerically) out by a factor of ten or more.
My review of the experimental situation, Double ccbar production in e+e- annihilations at high energy, is now available on the web as arXiv:0712.3138 [hep-ex]. If you want the short version: theory fought experiment, and experiment won. In principle this always happens, but the trick is to get it to work out in practice. And the short version is of course prejudicial: it was always possible that something had been neglected in the analysis (there were some ingenious suggestions), or that some mistake had been made. The rhetoric about a theory being thrown out the moment you see a piece of contrary data sounds unlikely --- or just plain wrong --- and indeed it is. If you want to get a feel for how this sort of thing really plays out, at least in my field, read on. I can't claim that it'll be accessible unless you have some particle physics, however.
(This paper is the long-overdue writeup of a review I presented at the International Workshop on Charm Physics, a meeting I helped organise at Cornell in August. I posted earlier concerning the future of charm physics, the panel discussion that closed the workshop.)