It seems that I should be able to readily compute U.S. market capitalization percentage of global capitalization using data reported from this page at the World Federation of Exchanges.
How can I do this?
The United States GDP as a percentage of world GDP is frequently between ~20% and ~30%.
A country's total market capitalization starts approximately at GDP and then is shifted up or down based upon inflation, bubbles, busts, etc.
Most large countries now have equity markets of some form, so the US's share of market capitalization is trending towards its share of GDP from the time where only a few countries had developed equity markets such as the US, the UK, and the Dutch.
Download the Excel report for the year you'd like to analyze. If you choose December, all months of that year will be available for analysis.
Then click on the Market cap sheet. Under the Americas exchanges header, for any month of interest, add the NASDAQ and NYSE values, then divide the sum by the WFE total and multiply by 100.
The most recent data available at the time of this answer was December 2012. At this time, the U.S. markets were responsible for 34.3% of world market capitalization.