Dr. Nick Bostrom of Oxford says: probably. The basic argument is thus: Suppose that it is possible to make simulations rich enough to fool its inhabitants into thinking they are real. Then such simulations are probably common, given the ease of using computational power. So we are probably living in one rather than in a "real" world.
But really such arguments are specious. Bostrom tries to rigorize his argument by postulating that posthuman civilizations run "ancestor-simulations", but they might just as well run some other form of simulation, perhaps one in which only one observer (you, dear reader, of course!) is self aware, and everyone else is simulated just enough to continue the illusion. In which case his formula is significantly off. So his postulate #2 ("any posthuman civilization is extremely unlikely to run a significant number of simulations of their evolutionary history (or variations thereof)") is in fact quite likely to be true - or maybe it is, how could we know? But once that one is true, the others' truth values become unknown. In fact, in any scenario in which #2 is not followed precisely, Bostrom's math stops working.
This is often the problem with anthropic-principle arguments, and this one is no exception. You might be living in a simulation, but this paper is not a convincing argument.
