The most recent Academic Ranking of World Universities is now out
The University of Minnesota ranks 28th in the World, 21st in the North American region, and 10th among US public universities (which can be compared with the oft-stated goal to be among the top 3).
Minnesota is behind UC Berkeley, UCLA, UCSD, Penn, Washington, Madison, UCSF, Michigan, and Illinois. Given four are really part of the UC system (and UCSF was once part of UC Berkeley), we can describe ourselves as the 7th best public university system in US.
These rankings try to apply a systematic way to compare what is largely subjective. What would be useful would be looking at who produces the most Ph.D.s that go on to teaching at universities that produce Ph.Ds, etc., analogous to Google PageRank.