"A weed is a plant that no one has yet found a use for" - I came across someone quoting this the other day, somewhere in the Mudcat threads, I think. I can't remember who's supposed to have said it.
Alternatively, and I thionk more accurately, a weed is any plant in the wrong-place - forexample, "I'm a lonely little petunia in an onion patch", as Gracie Fields used to sing. Selective weedkillers kill all the meadow-flowers, because they are counted as weeds.