NEW YORK (AP) — BlackBerrys across the world buzzed back to life Thursday, leaving customers outraged and threatening to cost the granddaddy of all smartphones more business when it’s already struggling to keep up in a crowded marketplace.

The three-day blackout interrupted email and Internet services for tens of millions of frustrated users and inflicted more damage on an already tarnished brand.

“I’ve been a pretty big BlackBerry advocate,” said Kate Jacobson, a student at Michigan State University. “But I’m done playing these games with you, BlackBerry.”

After using a BlackBerry for three years, she said the outage was the “last straw.” On Thursday, she got an iPhone.

Her unhappiness was shared by users across several continents. BlackBerrys in Europe, Asia, Latin America and Africa had been without email or chat messages since Monday.

In the U.S. and Canada, the outage was shorter, starting Wednesday. But many, perhaps most, of the world’s 70 million BlackBerry users were affected.

“When I woke up in the morning and had zero emails, I was like, ‘That’s impossible,'” Jacobson said. She had already endured problems with her BlackBerry Curve turning off at the wrong moments. It didn’t play videos well, either.

Research In Motion Ltd., which makes the phones and handles email traffic to them, said the system was steadily processing a vast backlog of stalled messages.

The company’s two CEOs apologized profusely. It was a break from the past, when outages of BlackBerry service merited only terse statements from the company.

Mike Lazaridis and Jim Balsillie said they had not made plans yet to compensate customers, but they were turning their attention to that question.

“Our priority right up until this moment (has been) making sure the system’s up and running,” Balsillie said. “We’re going to fully commit to win that trust back.”

It will take more than an apology to win back some Blackberry users. But RIM’s latest fiasco is unlikely to result in a mass exodus of its corporate and government clients.

BlackBerrys, like other imperfect business technologies, are deeply entrenched in commercial settings, and getting rid of them represents time and money that companies may be reluctant to give up.

Indeed, RIM may experience a slower, more subtle migration from its smartphone. Two types of people have kept the BlackBerry from sinking further into the oblivion of once-iconic but forgotten gadgets: corporate IT managers and aspiring young people in developing countries like India. Countries outside North America account for 54 percent of RIM’s revenue.

For big companies, BlackBerrys are still the gold standard in security. But employees keep chipping away at the power of IT managers by bringing in their own phones and tablets — iPhones, iPads or devices powered by Google’s Android software— and demanding to get their work email on them, said Ahmed Datoo, vice president of Zenprise Inc., which helps companies manage their cellphone fleets.

With each instance, the BlackBerry’s position in its core market is undermined.

In the April-to-June period of 2010, 19 percent of the smartphones sold in the world were BlackBerrys, while a nearly equal number, 18 percent, were from a variety of brands that use Google Inc.’s Android software, according to research firm Gartner Inc.

In the same three-month period this year, 12 percent of smartphones were BlackBerrys, while Android phones zoomed to 43 percent, outselling BlackBerrys more than three to one.

BlackBerry phones have not kept pace with the iPhone and its imitators, said Shaw Wu, an analyst at Sterne Agee.

A recently launched update of the flagship “Bold” model with the signature BlackBerry keyboard is selling well, he said, but an all-touchscreen model isn’t. It just doesn’t match up to the iPhone and Android phones.

“If someone really wanted a full touchscreen experience, why would they buy that? You have much better alternatives out there,” Wu said.

RIM launched a tablet computer, the PlayBook, this year. But like other iPad wannabes, it’s been a dud.

In the developing world, the low-end BlackBerry Curve has been the first smartphone for many. It works well on relatively slow cellular networks, which means carriers are happy to push it, knowing that it won’t overwhelm them, said analyst Matthew Robison at Wunderlich Securities.

But that’s being threatened now that even Third World phone companies are upgrading their cellular networks to broadband speeds. That means Web browsing and multimedia will be sexy new applications — things the Curve does not do well compared with inexpensive touchscreen phones.

“I think it will be tougher for RIM to compete for the emerging-markets consumer,” Robison said. That, he thinks, is a bigger challenge for the company than the outage.

And in North America, the “brand damage is already done,” Robison said. RIM’s inability to keep up with the times means BlackBerrys could soon be quaint reminders of that early flush of excitement about reading email on the go.

The outage started when a crucial traffic-routing computer in BlackBerry’s European network failed. A backup also failed.

Although the underlying issues were quickly repaired, the system had built up a backlog of emails and messages that needed to be released.

Meanwhile, messages destined for the affected countries were piling up at BlackBerry data centers in the rest of the world, slowing service everywhere. Then the outage spread to the U.S. and Canada.

Among smartphones, BlackBerrys are uniquely tied to their manufacturers.

BlackBerrys get their email through RIM’s centralized setup, allowing the company to offer a high level of security that appeals to corporate IT managers. But when something goes wrong, it affects millions of people at the same time. Blackouts are not localized to one company or one carrier, as other outages are.

Such a widespread, highly visible failure could threaten RIM stock. But investors have taken the outage in stride. The stock is down less than 1 percent since Friday’s close.

That’s because RIM’s stock is already so beaten down by other bad news. It’s lost 83 percent of its value from its peak three years ago — the time it’s taken for BlackBerrys to go from hot items and status symbols to near-has-beens.