Different university rankings abound, but this one's methodology has some merit (anonymous survey of 17,000+ academics worldwide).
The Alumni Association states:
U-M has been ranked 12th in the annual Times Higher Education World Reputation Rankings. The 2012 Reputation Rankings are based on results from an invitation-only survey of scholars from around the world. The University is one of only three public institutions in the top 15—the others are the University of California, Berkeley (5), and the University of California, Los Angeles (9).
(See official Michigan release here: http://www.ur.umich.edu/update/archives/120315/rankings .)
The survey results are here: http://www.timeshighereducation.co.uk/world-university-rankings/ .
Other B1G representation (based on reputation) includes Northwestern (26th), Wisconsin (27th), Illinois (31st), Minnesota (42nd), Ohio State (57th), MSU (96th) and Purdue (98th). Good showing for Michigan and the B1G!