
A few days ago The New York Times did a story on Berea College in Kentucky, a college founded in 1855 that does not charge tuition. That's right--if you get accepted into Berea and matriculate, you don't pay a dime in tuition (and they are ranked #75 among small liberal arts colleges according to U.S. News and World Report--which we should all take with a grain of salt, these rankings, but figured I'd include them for what they are worth).
This is a description of Berea from their college website:
Berea College is distinctive among institutions of higher learning. Founded in 1855 as the first interracial and coeducational college in the South, Berea charges no tuition and admits only academically promising students, primarily from Appalachia, who have limited economic resources. Berea’s cost of educating a student exceeds $23,000 per year.

[View of sunset from Berea college athletic fields]
According to their "About the College" site, 1 in 3 students at Berea are also members of an ethnic minority. So here we have a college that is free, that was the first interracial and coeducational college to open its doors in the South (and this during a time well before the likes of Brown vs. Board of Education and well before places in the South like Vanderbilt and Sewanee were opening its doors to African Americans and women), and whose mission is to educate promising students who wouldn't normally be able to afford the exorbitant tuition and cost of living at places like Harvard, Swarthmore, and Stanford.
That, is truly a Great Impossible Feat.