U.S. stocks are on the verge of surpassing their longest-running rally, ratifying a market rebound that began in the ashes of the financial crisis and defying those who have questioned its staying power.

Wednesday will mark 3,453 days since the S&P 500 hit its low of 666 on March 9, 2009. Since then, the broadest U.S. blue-chip index has more than quadrupled in price terms, creeping within striking distance of its January all-time record and outpacing most rival major global indexes.

The...