There's no Matrix you dummies! This guy is just a really clever Martian who can do good special effects. Is there a way to prove otherwise?
Most discussion of simulation arguments, from Descartes to Bostrom, has focused on trying to prove that we're NOT in a simulation, concerned that we don't see the world (enough) as it is. There is some profit in pointing out that "simulation" is ill-defined, and because of the way our senses filter and bind and create our experience, the distinction between a simulated world and the "real world" is somewhat arbitrary. Therefore, perhaps a more interesting question is what it would take for us to be convinced that we ARE in a simulation, if one of the simulation programmers appeared in our midst, and prove to us that this IS a simulation. What kinds of experiences or information would the revelations of the simulation programmers have to contain to make us think that we're in a simulation?
1) First trick would be for the simulators to demonstrate violations of physical laws at their will. Then again, an apparent violation of physical law could just be the result of advanced technology that you don't understand. "Look! Gravity reversed itself locally! Look, we changed it so you're surviving in vacuum just fine, and now I just ran time backwards and separate causes and effects, but only on your street! Obviously you must be in a simulation!" Right? Certainly such behavior of the world would be inconsistent with our current understanding of how things are supposed to work, but does that automatically mean it's a simulation? Maybe it's just aliens with Clarke's Third Law-level technology, and they're screwing with you. And for that matter, shouldn't we expect that there are limits on what even a simulator can do without the simulation no longer functioning? The source code of World of Warcraft is certainly not robust to any possible manipulation you could dream up.
2) They could show you (a la Thirteenth Floor) where the simulation breaks down at some boundary (scale, time, space, cognition). But would that prove it? We know already that there are such boundaries (uncertainty principle, the Big Bang, cognitive closure at least in the trivial sense of limited working memory), yet no one has seriously argued that this means we're in a simulation.
3) They could tell you what you're thinking, or tell you a 20 digit number you wrote on a piece of paper in your desk (and didn't tell anyone), if they really have access to the entire code of the simulation (and they could just stop it and do a CTRL-F). Then again, how do you know they're not aliens with awesome fMRIs or paper-reading X-ray machines?
4) They could do something fatal to you, and then have you re-awake. Again, maybe they have great technology! Even if they do something that would physically destroy your nervous tissue like drop you into a volcano and you wake up, maybe you're just waking up for the first time with memory implants (of a life up to and including falling into a volcano), or maybe there's a way to recover consciousness even after such total tissue destruction that we don't yet understand.
5) They could demonstrate continuity of experience; that is, one second you're walking around what you thought was 21st century Earth, the next you're being unplugged from the computer in your vat. How do you know the vat isn't the simulation? Even if there's no simulation technology being used here, a lot can be done to manipulate perception of time; and for that matter, maybe you're a clone with memory implants, and you're really waking up in that vat for the first time, with false memories.
So: are there tests that could even in principle separate simulators who create our universe, from mere clever aliens who co-inhabit it with us?
[Added later: Michael Shermer makes an interestingly analogous argument when he states, in a variant on Clarke's Third Law, that a sufficiently advanced alien would be indistinguishable from a supernatural being. In a predictably miffed answer, a counter-arguer misses some points, saying that the absence of recognizable modern telecommunications devices from the Bible shows that we can distinguish gods from aliens. Apparently the counterarguer insists that aliens use cell phones.]