The Simulation Argument is discussed at George Dvorsky's sentient developments, after being mentioned in an article yesterday by John Tierney in the New York Times. It's due to Nick Bostrom, whose original paper is available online.
The argument is as follows: "posthumans", that is, the people of the future who have much better computers than we do, will use their computers to run simulations of, well, more primitive humans. These simulations will be so detailed that they include a working virtual nervous system for all the people inside. And you have to figure that they're not going to run just one of these simulations; the future people run these simulations for fun! (This seems reasonable; I've spent way too much time playing SimCity to argue against this.) So we should expect that over the lifetime of humanity there are a very large number of such simulations being run, and that it is therefore very unlikely that we live in the "real world".
For me, this bears a superficial similarity to Pascal's Wager, although the mathematics is different; for one thing, Pascal's Wager involves an infinite payoff and there are no infinities here. But it's probably useful to think of there being effectively an infinite number of these simulations, in which case the probability that we're living in the "real world" turns out to be essentially zero. (Bostrom doesn't go this far; he says he feels there's about a 20 percent chance we're living in a computer simulation, which basically means he figures there's a 20 percent chance that civilization gets to the simulated-reality stage, if you neglect the probability that there are simulated realities but we're in the real one.) I suspect the real reason this reminds me of Pascal's Wager is because it seems natural to equate the runner of the simulation with "God".
What's especially strange, at first, is the idea that the simulations could have simulations within them. This reminds me of a cosmological theory that universes "evolve" by spouting black holes; in this theory, black holes are connections to other universes, where the various physical constants are slightly different than in the parent universe; thus there's a sort of Darwinian selection for universes, where the selective pressure is towards making lots of black holes. (Then why don't we live in a universe with lots of black holes?) As to the simulations within simulations -- if you carry this to the logical extreme, we are likely to live in some very deeply nested simulation. The problem is that infinite nesting probably isn't possible. And does the level of nesting even matter? My first instinct is to think that nested simulations would necessarily be of "lower fidelity" than first-level simulations, but since everything is digital this need not be true, as Bostrom himself points out. However, he also points out the disturbing fact that since a posthuman society would require more computing power to simulate -- you've got to simulate what all the computers are doing quite well -- if we head towards being posthuman we might be shut off! Personally I would like to think that the ethics of these simulations require the Simulator to not just shut us off. Presumably the person running the simulation could get on some sort of loudspeaker and let us know what was going on. (Although that might raise other ethical questions -- do simulated realities have some sort of Prime Directive, where you're not supposed to interfere with them?)
The mathematics of the argument seems so simple, though, that I'm almost inclined to throw it out on those means alone, along with other things likes Pascal's Wager and the Copernican principle. Surely proving the existence of God (and that's what this is, although people don't put it this way) can't be so easy!