According to ABC News, RIM confirmed Wednesday that the outages spread to North and South America, the only major areas unaffected as of Tuesday.
Some Twitter users in Canada reported service outages as well.
As the outages stretch into their third day, Research In Motion Ltd., the Canadian company that makes the phones, said Tuesday that a crucial link in its infrastructure had failed, and a backup didn't work either.
"We are now working to clear that backlog and restore normal service as quickly as possible," the company said in a brief statement.
Unlike other cellphone makers, RIM handles email and messaging traffic to and from its phones. When it encounters a problem, millions of subscribers are affected at once.
The Associated Press contributed to this report.