UMich has decent merit-based aid packages. They have quite a few full ride offers and several awards in the $10K+ range.

I heard about a girl turn down an offer to go to Harvard because of a full ride to UMich.

There are at least 5-10 highly coveted full tuition scholarships at all the major universities. Some require just applying to the university itself while others will ask that you complete a separate application for the scholarship specifically.

A quick blurb about top scholarships that I know of from the colleges that I applied to:

Georgia Tech - the Presidential scholars program requires an application and a series of interviews. If you land the prestigious scholarship, you get full tuition plus fees, and you get stipends for additional help.

University of Georgia - the Foundation Fellows program is full tuition and fees. Plus, you get study abroad stipends so that you can travel every summer to a new destination. I've heard friends take trips to New Zealand, China, anywhere.

Vanderbilt - the Lanier scholarship is 2/3 or full tuition to Southeastern HS students.

Emory - the Scholars program equals full tuition.

All of that said, look around for as much information as possible.

In addition to those listed by poodlez, Wash U. in St. Louis offers merit based scholarships - "awards range from annual awards of $2,500 to half-tuition scholarships to full-tuition scholarships ($34,500 in academic year 2007-08) with annual stipends."

http://admissions.wustl.edu/admissions/ua.nsf/3rd%20Level%20Pages_Scholarships_scholarships.htm?OpenPage&charset=iso-8859-1