Sometime long ago, someone started a speech with, “The Famous So-And-So once said, ‘blah blah blah.’” And so began a very, very long love affair with starting speeches and essays with quotes from other people.
I can’t completely condemn the practice, because sometimes people do it well. But it’s only well-done if the quote you’re using really does have a great deal to do with what you’re writing about. Don’t quote “I Have a Dream” if your dream is simply getting enough scholarship money to pay your sorority dues for an entire year. Don’t quote FDR’s “The only thing we have to fear is fear itself” if the fear you’re writing about is the fear that you wouldn’t get early acceptance to Boston University. That’s not using a quote, it’s abusing a quote.
If you quote JFK’s “Ask not what your country can do for you, but what you can do for your country” because you’ve decided to join the military (or an ROTC program, perhaps) knowing of our mounting Middle East presence and the international threats we face in the 21st century, then that’s a meaningful quote. In that case, you’re the very embodiment of the quote you chose, and that’s how using quotes ought to be done.
But just ask yourself before you start with a quote: Am I doing this because it applies to me, or just to bolster my essay and sound smarter by quoting someone famous?