The tech giant's status page showed the App Store, iTunes, iBooks store and Mac App store went down from 0900 GMT.
Similar outages were seen in Apple online services in Britain and France. The Next Web, the international technology news site, said it had reports of outages affecting more than 40 countries.
Apple's iCloud and mail services were also down, but appeared to have been restored after around four hours, according to the status page.
Other services such as FaceTime, messaging and Apple TV did not appear to be affected.
Apple did not immediately respond to an AFP request for comment.
Apple support forums included complaints from users around the world, including the Netherlands and Iceland, unable to install or update apps.
Reddit forums mentioned problems from users in Britain, Australia and elsewhere.
The news comes two days after Apple announced details of its smartwatch, which will be available in several markets on April 24, along with a new Macbook computer.
Apple said at the event that it has sold more than 700 million iPhones since launching the device in 2007.
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