Leonard E. Burman, William G. Gale, Jeff Rohaly (all of the Urban Institute) have published The Expanding Reach of the Individual AMT on the Tax Policy Center web site. Here is part of the abstract:

In January 1969, Treasury Secretary Joseph W. Barr informed Congress that 155 individual taxpayers with incomes exceeding $200,000 had paid no federal income tax in 1966. The news created a political firestorm. In 1969, members of Congress received more constituent letters about the 155 taxpayers than about the Vietnam war. Later that year, Congress created a minimum tax to prevent wealthy individuals from taking advantage of tax laws to eliminate their federal income tax liability.

Both the original minimum tax and its successor, the individual AMT, have applied in the past to a small minority of high-income households. But barring a change in law, this "class tax" will soon be a "mass tax." Current projections show the number of AMT taxpayers skyrocketing from one million in 1999 to almost 31 million in 2010. Without reform, virtually all upper-middle-class families with two or more children will be paying the AMT by decade’s end. The AMT is notoriously complex, and its record on fairness and efficiency is mixed at best. But because of its widening reach, fixing the AMT will be expensive. By the end of the decade, repealing the AMT will cost more than repealing the regular income tax. This paper explains how a tax originally designed to target 155 taxpayers could grow to cover 31 million, discusses economic issues related to the alternative minimum tax, and examines options for reform.