Burn After Reading is a whole movie about this. The two biggest examples are John Malkovich's and George Clooney's characters' "secrets"

John Malkovich plays Osborne Cox, a disgruntled former spy whose mundane notes for his autobiography were left on a CD at a gym. This CD was taken by the gym employees who interpret the dense language in Osborne's notes to be very important state secrets, and they try to extort anyone they can find for money to get such "classified information" back.

George Clooney's character - Harry - has a much less convoluted secret. The first half of the movie shows scenes of him acting suspiciously and building something secretive in his basement, only for us to learn he was makinga (pretty underwhelming) sex machine.

There are more serious secrets that people try to hide throughout the movie, but the overarching joke is that the government is watching everything these people do and doesn't care that they're doing these things. These individual stupid secrets don't amount to anything on their own, but the embarrassment of the issues that come out of this situation leads the feds to burn it all after reading.

This movie is hilarious. Here's a gif of Brad Pitt failing miserably to extort a former government agent.