"If you hide it you risk being discharged a month, a year, or five years from now when your employer finds out, and then they aren't referenceable."

This, this, a million times this. It's not even losing the job that would be the worst for me, it would be the paranoia of turning up to work every day thinking "Did they find out about that thing now? Are they considering firing me or did they decide it didn't matter? Argh!!".

There's a Calvin & Hobbes strip where Calvin breaks his dad's binoculars and is certain at the dinner table that night that his father knows. The anxiety gets to Calvin so much that after about 30 seconds (this is Calvin, remember) he breaks down and confesses. That would so be me in an employment situation where there was something I hadn't disclosed which could lead to dismissal.