Yeah, you've got to fess up. The only way you might get away with keeping an overpayment of wages is if it wasn't reasonable for you to notice (i.e. it was just a few quid a month or something).
In answer to the original question, if I got a 20k pay rise I would probably spend it on poker
The missus was overpaid quite a few years back during her sandwich year at uni with Norwich Union. Basically, they paid her an extra month. When she received the money, she contacted them to ask if it was correct or not (she honestly didn't know when the final month's pay was coming in, but had thought this one was in error). She eventually got through to someone in accounts who rudely told her she'd be paid what she was due.
So, as poor students, we thought nothing more of it, they'd told her that she'd receive the correct amount - and she'd made the effort to check and return the money if it was an error.
Then about 3 months later she received a formal letter requesting the money to be returned. We didn't have the money any more, but spoke to citizen's advice and a solicitor friend. We were basically told that the law is vague in this area but the main point is that if you weren't aware that the money wasn't yours, and if you'd be in a worse position if you had to pay the money back than you would have been if you hadn't received it in the first place, then the law is on your side - and what often happens in this case is that you pay it back within your means, and for a non-earning student this would have been about £3 a week...
Anyway, we stuck to our guns, and wrote a letter back explaining the situation. Norwich Union wrote off the amount.
Not sure if that's always the case, but that's what happened to us.
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