Yeah, the smart thing is to let someone know. You can easily go to prison for keeping it.
It's easy to say "Oh, I'd just run for it!" but you'd never actually get any of it out. What are you going to do? Withdraw it from an ATM? You can't transfer it, with that large a sum it would have to be cleared by someone at the bank first. They're going to want to know where it came from.
Too many possibilities for things to blow up. I'm happy enough with my current income, that I wouldn't be crushed if/when the error was corrected. However, if it turns out I can keep it (unlikely, but then again $1M showing up in a my bank account is pretty friggin' unlikely too), then I could do it with a clear conscience.
Now what I would do with $1M is something else entirely. Boring, though. Invest that shit in a [a href="http://en.wikipedia.org/wiki/Certificate_of_deposit"]CD[/a]. Those things are compounded daily, so I could just live off the interest.