Stanford is accused of lying about the safety of investments he sold as "certificates of deposit" (CDs) and promising unrealistically high rates of return.
Regulators also allege he forged historical data about other investments which he then used to lure in more investors for his products.
The whereabouts of Stanford, a wealthy billionaire from Texas, remain unknown, the SEC has said.
In Venezuela, the nation's banking regulator reassured customers that the country's own Stanford Bank Venezuela was healthy and not affiliated with the US firm.
|Stanford's US offices were raided
on Tuesday [Reuters]
In the twin-island state of Antigua and Barbuda, where Stanford is the biggest private employer, Baldwin Spencer, the prime minister, said the SEC charges could have "catastrophic" consequences, but urged the public not to panic.
But in Antigua's capital, St John's and the Venezuelan capital, Caracas, hundreds lined up outside Stanford banks and offices.
"I heard the news and came straight down. We've had money here for two years and I want it back," Josefina Moreno, who said relatives had invested money with the firm, told the Reuters news agency.
In Mexico City, Mexico, about 40 people waited outside a Stanford office for information, demanding to be let in, while in Peru, regulators reportedly sent an inspection team to local Stanford offices.
Stanford International Bank has affiliates in Mexico, Panama, Colombia, Ecuador, Peru and Venezuela.
Stanford, 58, is one of the most prominent businessmen in the Caribbean, with a personal fortune estimated at $2.2bn by Forbes magazine.
A fan of cricket, Stanford developed the Twenty20 competition in the Caribbean and last November held a $20m game between England and his own team made up of West Indian players.
The England and West Indies cricket boards have suspended sponsorship negotiations with Stanford following the fraud charges.
The charges are the latest to be brought after an increase in scrutiny by investors, politicians and regulators on the returns promised and provided by investment firms, following the massive alleged $50bn fraud by Bernard Madoff, the Wall Street financier.
Stanford's investment companies were exposed to losses from the alleged "Ponzi" scheme run by Madoff, and the SEC alleged that it falsely reassured investors that this had not been the case.
A Ponzi scheme typically pays older investors "returns" from money brought in by newer investors, rather than from real investment returns.