Certainly, there are many phrases and sentences quoted from Shakespeare's Hamlet. These phrases, of course, were not trite or overworked until people began using them in the unoriginal manner of repeating what they have heard. As Bernard Levin in his book Enthusiasms declares, Shakespearean phrases "remain alive in his mouth even if they do not in ours. So, cliches do, indeed, point to lack of originality on the part of the modern speaker/writer.
Here are some from Hamlet,
"neither a borrower nor a lender be"
"the lady doth protest too much"
something is "rotten in Denmark"
"sweets for the sweet"
"The time is out of joint"
"every dog has its day"
"To be, or not to be"