In "Are You Living In A Computer Simulation?" Philosophical Quarterly, Vol. 53, No. 211, pp. 243-255 (2003), Bostrom reasons that at least one of the following three propositions (paraphrased somewhat by me) must be true:
(1) It is almost certain that a society like ours would never develop sufficient technology to create "ancestor simulations" inhabited by conscious simulated minds.
(2) Any society capable of running such simulations is extremely unlikely to run them.
(3) You are almost certainly living in a simulation.
Why? In essence, Bostrom hypothesizes that a technology capable of running such simulations at all would be capable of running an astronomically large number of them. Furthermore, if such simulations are accurate representations of their creators' precursor societies, their simulated inhabitants will of necessity develop the virtual technology to create their own ancestor simulations, which will in turn spawn their own simulations and so on, subject only to the computational constraints of the machine on which the first-order simulation is running.
Thus, if such simulations have ever been or will ever be created (i.e. if propositions (1) and (2) are false), the minds living in simulated pasts would vastly outnumber the "actual" minds living in their "true" presents. Consequently, the odds would be very strong that yours is one of the simulated minds.
One could suppose superficially that, even if (1) and (2) are false, you could be living in an "actual" present wherein the technology to simulate minds has not yet been invented. But because the number of simulated minds taken across all of time will likely exceed the number of actual minds--and because you in principle have no means of distinguishing between an "actual" present and a simulated past that you experience as the present--the odds of yours being one of the comparatively few "actual" minds to experience reality the first time through are pretty long.
So how likely is it that propositions (1) and (2) are false? That is, how likely is it that we are living in a simulation? Bostrom believes that we lack sufficient information to choose meaningfully among the three propositions. We cannot at this point predict whether a society on its way to developing the necessary technology would most likely destroy itself in the process, e.g. via a doomsday weapon. We also cannot predict whether the social forces that would preclude the running of ancestor simulations--e.g. a civilization-wide lack of interest or a universal agreement on the immorality of doing so--are likely to develop in a society otherwise capable of running them. Bostrom notes that in this latter case the agreement (or enforcement against those who disagree) would have to be nearly universal, since even a very small number of nonconforming individuals would be sufficient to create an astronomically large number of simulations.
Given our present ignorance, Bostrom suggests that we have little choice but to assign equal likelihood to each proposition. Thus, assuming Bostrom's reasoning to be sound, the odds are about one in three that you are living in a computer simulation. Bostrom since has stated that he personally believes the odds to be around 20% because he slightly favors the truth of proposition (2), but stresses that this is a matter of subjective belief. Based on the information currently available to us, he proposes, we have no strong evidence for or against any of the three hypotheses and must assign them equal credence.
Fortunately, Bostram thinks that even if you are living in a computer simulation you don't have to do much about it. With a few subtle exceptions, an ersatz reality presents no significant operational differences from the genuine article. This should be a relief if you were worried that you weren't up to messianic adventure involving jujitsu, automatic weapons, and two lame sequels.