John Wheeler probably wins the prize for pithiest summation (and one of the best): “The reason Universities have students is so they can teach the Professors” (quoting from memory)
Via Lance Fortnow, a thought-provoking speech by UCLA Professor Andrew Kahng on the role grad students can play in a University.
Of course, neither of these tells the whole story, by a long shot. But they’re both pretty worthwhile ideals.