"Eighty-two of America’s largest and most profitable corporations paid no federal income tax in at least one year during the first three years of the George W. Bush administration — a period when federal corporate tax collections fell to their lowest sustained level in six decades. This is one of the many troubling findings of a major new report on corporate tax avoidance by Citizens for Tax Justice (CTJ) and the Institute on Taxation and Economic Policy (ITEP). The report covered 275 profitable Fortune 500 corporations, with total U.S. profits of $1.1 trillion over the three-year period."
http://www.ctj.org/corpfed04pr.pdfhttp://www.ctj.org/corpfed04an.pdf (full report)
Of course, according to
this article, "More than half of US corporations paid no federal income taxes during the boom years of the late 1990s, and those that did were able to shelter much of their income, according to congressional accountants."
hope this helps
edit: 'Offshore tax sheltering', i.e., Bermuda, is addressed in the full-report link above, Report Page 11/pdf page 15 of 72.