The swoop came after a two-year undercover FBI investigation spanning four continents.
Operation Card Shop tracked those buying and selling information through a fake, FBI-run online forum on such "carding" schemes.
Twelve of the arrests were in the United States, with six in the UK.
All of the detained are men ranging in age from 18 to 25. Some face 40 years in prison if convicted on fraud-related charges.
One of the men, Mir Islam, known online as "JoshTheGod", was charged with trafficking in 50,000 stolen credit card numbers.
In total, investigators notified credit card providers of more than 400,000 compromised accounts.
US officials said the operation prevented losses of $205m (Â£131m) from debit and credit cards.
The sting focused around an online forum called Carder Profit, set up by the FBI in June 2010, where users could exchange stolen account and card numbers.
Investigators identified alleged cybercriminals in the US, Europe, Asia and Australia.
US district attorney Preet Bharara  
          said in a statement
: "Clever computer criminals operating behind the supposed veil of the internet are still subject to the long arm of the law."
At least 24 people in 13 countries have been arrested in a US-led sting operation targeting illegal trafficking of credit card information.