There are no public APIs for doing this. You could remove it by examining the view hierarchy and removing the view as some have suggested, but this would be very risky.
Here's why it's a bad idea:
If Apple doesn't have an official API for removing the bar, they may have good reasons for doing so, and their own code may rely on it being there. You might not ever encounter a problem because you do all your testing (for example) on an English keyboard. But what if the view you are removing is required for entry in another language, or for accessibility purposes? Or what if in a future version of iOS their own implementation changes such that it assumes the view is always there? Your code will crash, and you'll be stuck scrambling to get an update out while frustrated users wait for weeks.
Interestingly, Remco's appended answer proves this point. On iOS 6.0.1, a change was made that required a fix to the hack. Anyone who had implemented the hack for ios 5 would have been forced to do an update as a result. Fortunately it was only an aesthetic change, but it could have been much worse.