Queues wound down the street in Sydney, Tokyo, London, Paris and Munich as fans gathered to get their hands on the iPhone 4S, ahead of later store sales in North America.
"I am a fan, a big fan. I want something to remember Steve Jobs by," said Haruko Shiraishi, waiting patiently with her Yorkshire terrier Miu Miu at the end of an eight block queue in Tokyo's smart Ginza shopping district.
The new model looks similar to the previous iPhone 4 but has an upgraded camera, faster processor and highly regarded voice-activated software, which allows users to ask questions.
"It's like your own personal secretary," said Shane Gray, 42, in Sydney.
The phone -- introduced just a day before Jobs died -- was initially dubbed a disappointment because it fell short of being a revolution in design, but glowing reviews centered around its "Siri" voice-activated software have helped it set a record pace in initial, online sales orders.
Apple CEO Tim Cook and his executive team hope the first device sold without their visionary leader at the helm will protect them against a growing challenge from the likes of Samsung Electronics.
The South Korean firm, Apple's arch-rival with smartphones powered by Google's Android software, expects to overtake it as the world's biggest smartphone vendor in terms of units sold in the third quarter.
"(Jobs) made everything better and the products he released were thought through in such detail," Duncan Hoare in London said, after a loud roar greeted the opening of the store.
"It was about the beauty of something and the simplicity."
Apple does not release sales figures on launch day, so gauging initial sales is difficult. However it took more than 1 million online orders in the first 24 hours after its release, exceeding the 600,000 for the iPhone 4, though that model was sold in fewer countries initially.
"Despite the initial disappointment that this wasn't an iPhone 5, the reality is we're still seeing the usual frenzy that we've got used to on launch day," analyst Ben Wood at CCS Insight told Reuters, adding that analysts expect a few million phones to be sold globally on the first weekend.
Unlike many in Tokyo, shoppers in European cities told Reuters they wanted the phone because it was a 'lifestyle choice' and not necessarily a tribute to Jobs.
"I need a new one since my dog destroyed my old 3GS," said Gaby Wunder-Sambale, 45, shivering in Frankfurt.
Despite the enthusiasm at Apple stores, the launch was marred somewhat by widespread complaints this week on the Internet about problems downloading iOS 5 -- the latest version of Apple's mobile software.
There were also problems with iCloud, Apple's online communications, media storage and backup service formally launched on Wednesday, with users reporting glitches such as losing their email access.
Queues in Paris were smaller than those normally seen at an iPhone launch, with some fans there wondering if the somewhat underwhelming launch had put people off, but in London and elsewhere the queues were as large as ever.
On Regent Street in central London, the queue wound down a sidestreet and into a park, where Starbucks had a mobile stand to serve coffee. Of the 40 people to whom Reuters spoke in London, 13 were switching from other phones.
"This is rubbish," one buyer at a north London store said, holding his Blackberry after owner Research in Motion struggled for days to fix an international outage of its Blackberry email and messaging services.
JOBS SHADOW OVER iPHONE LAUNCH
The vast majority of the iPhone 4S buyers Reuters spoke to in Sydney, France and Frankfurt were existing Apple customers, many having bought the original iPhone and subsequent upgrades.
"Since Jobs died, I wanted to make sure I had a new iPhone with some advantages over the old," said iPhone devotee Mark Du, concerned about future gadgets without Jobs in charge.
Apple fans in Sydney, Tokyo, Frankfurt and London made sure Jobs was part of the iPhone 4S launch, with flower, candle and photo shrines to the late Apple boss erected outside the stores. A black and white picture of Jobs in Covent Garden carried the line "Let's make a dent in the universe."
Underscoring the enthusiasm for the new phone, Japanese mobile carrier Softbank Corp had to temporarily stop contract applications after its computer system was overwhelmed with more requests than it had expected.
Some analysts expect fourth-quarter iPhone shipments to reach 30 million or more, almost twice as many as a year ago.
Apple's fifth-generation iPhone uses chips from Qualcomm Inc, Toshiba and a host of smaller semiconductor companies, according to repair firm iFixit, which cracked the device open on Thursday.
The iPhone -- seen as the gold standard for smartphones -- is Apple's highest-margin product and accounts for 40 percent of its annual revenue.
Analysts point to several factors in Apple's favor: a $199 price that matches up well with rival devices; availability promised on more than 100 carriers by the end of 2011, far more than its predecessors; and glowing reviews.
(Additional reporting by Michael Perry in SYDNEY, Edwin Chan in LOS ANGELES, Isabel Reynolds in TOKYO, Marie Mawad in PARIS, Jens Hack in MUNICH, Christoph Steitz in FRANKFURT and Giles Elgood, Matt Cowan and Kate Holton in LONDON; Editing by Mark Bendeich, Alex Richardson and Sophie Walker)