Never throw any writing away, especially not homework. As friends and long-time readers know, I returned to college as an adult and finally graduated with a B.A. in Professional writing in 2005. I was 48.
Because I'm a writer, I kept every essay and term paper. A couple of the things I wrote for my various classes have since been published, and it's about to happen again.
An argumentative essay I wrote in the form of a letter back in March 2004 just found a home in an anthology of unsent letters, making it my 32nd acceptance of the year.