Nick Bostrom, Director of the Future of Humanity Institute at Oxford, says in a New York Times article today:
“My gut feeling, and it’s nothing more than that,” he says, “is that there’s a 20 percent chance we’re living in a computer simulation.”
Bostrom thinks so because, barring a future prohibition on creating simulated worlds or disinterest in doing so, that our posthuman descendants are almost certain to create simulations of the past. The more simulations that are run, the more likely that you are in one.
By some estimates, there will be enough available computing power to create a simulated world by 2050.
However, there could be a recursive problem:
It’s also possible that there would be logistical problems in creating layer upon layer of simulations. There might not be enough computing power to continue the simulation if billions of inhabitants of a virtual world started creating their own virtual worlds with billions of inhabitants apiece.
I wouldn't count on it though.
Source: Tierney, John. "Our Lives, Controlled From Some Guy's Couch." The New York Times, 14 August 2007, D1, D4.