10 years ago this was a real problem. Now it just takes a few calls to clear everything up, and a few weeks for it to all get sorted out. Yeah, it sucks you have to waste hours on it, but the credit agencies have a procedure for identity theft reporting now.
If you're ever worried something might happen, just flag your account for fraud. Once you do that, opening any new accounts will require they call you to confirm (which should be the default IMO).
Of course, the real problem is that we're all far to much in the habit of borrowing money, but that's a different rant.