You could almost make a presentation on the subject of "famous lines from Hamlet that have become well-known sayings in English."
Here are a few. Often they have gotten completely separated from their actual meaning in the play, but people say them anyway.
"Something is rotten in Denmark." People will say this of any bad smell, meaning it is so bad that it can be smelled from thousands of miles away! It's a misquotation of "Something is rotten in the state of Denmark."
"The play's the thing."
"Alas, poor Yorick. I knew him, Horatio." (Often misquoted as "I knew him WELL, Horatio.")
"The lady doth protest too much, methinks."
"Speak the speech trippingly on the tongue." (Slight misquotation and shortening of the correct line, "Speak the speech, I pray you, as I pronounced it to you, trippingly on the tongue.")
"Very like a whale."
"A hit, a very palpable hit."
"Good night, sweet Prince, and flights of angels sing thee to they rest!"