What's the phrase that is commonly used after someone says or does something embarrassing/funny that you won't let them forget?

Solution 1:

You are not going to live this down

If you say that you will never live down something bad or embarrassing that you have done, you mean people will not forget it Three million people saw the singer fall off the edge of the stage. He'll never live it down. I'll never live down the fact that I spilt champagne down my boss's trousers.

never live down. (n.d.) Cambridge Idioms Dictionary, 2nd ed.. (2006). Retrieved March 18 2017 from http://idioms.thefreedictionary.com/never+live+down

Solution 2:

You might be thinking of holding it over someone's head.

hold over someone's head (transitive, idiomatic) To harp on; to remind continuously (especially of a misstep or defeat) I get one parking ticket and he holds it over my head for six months. - wikitionary