I have a duty to my namesake to bring this up :-) Peter Cooper (the 19th century industrialist and Presidential candidate - not me) pioneered the tuition-free education concept in the United States with the Cooper Union, which is still running today: http://en.wikipedia.org/wiki/Cooper_Union - online universities are cool, but the Cooper Union is a full-on bricks and mortar college.
I went to Cooper Union for a year, and it's a freaking awesome school; besides having excellent classes (at least in engineering, don't know about art/architecture - it only has those three programs, so don't even think about it otherwise), it really is zero-tuition, no strings attached. I highly recommend that any engineering/art/architecture students apply, at least if you think you have a shot of getting in. They are not a "by-the-numbers" type of school, and they definitely have room for people with colorful backgrounds, even at the engineering school - just make sure your math is solid!
There is one hidden cost, though - you're going to be paying out the ass to live anywhere near the Village, and New York City is expensive. That was the main reason that I left. Well, that, and the fact that I realized after a year that engineering wasn't for me - it's not an engineering school in the MIT sense, where you're still going to be satisfied even if you're interested in pure physics or math, Cooper Union really is a school devoted to teaching you to be a practicing engineer.
Still, it beats the hell out of NYU or any of the other schools around, where you're paying both the exorbitant NYC apartment costs plus 40k/year for tuition, so it should definitely be on any engineer's list...
There is also Olin College, outside Boston. In fact that's what I thought this article was going to be about. It's only a few years old but it has a good reputation already.
Stanford, too, was founded as a tuition-free school. Sadly, they were forced to begin charging tuition in 1920.
The good news is that, a century later, the school is returning to its roots by offering free tuition to students whose families make less than about $100k per year.