Becoming the world's biggest company was a milestone for the iPhone maker, but can it stay on top?

When Apple's chief executive Tim Cook takes the stage at the Moscone Centre in San Francisco on Monday, he will face one key question: can Apple do it again? Can the company that upended the phone business with the iPhone in 2007, and made tablets an everyday item used by millions with the iPad in 2010, find a new must-have product – a fresh leap of innovation?

The audience, thousands of developers who write apps for the iPhone and Mac, will be eager to know: their income relies on Apple getting its products in front of people. But for Cook and his executives the mutterings are growing louder before the Worldwide Developers Conference (WWDC) that Apple just isn't innovating any more, since the death in October 2011 of Steve Jobs, its co-founder and Cook's predecessor.

To counter that, Cook and his team are expected to announce a "smart home" initiative, whereby an iPhone or iPad will be able to interact with lighting controls, heating systems, air conditioners and appliances, as well as a "Health Book" software for future versions of the iPhone that will gather personal health data – perhaps through some sort of unrevealed wearable technology.

But is that enough? Apple's backers can point to its being the most valuable company in the world. Apple's revenues and profits outstrip the combined totals for Microsoft and Google; and iPhone sales are nudging 10% of the mobile phone market (including even the cheapest handsets), just behind once-dominant Nokia, though some way behind its bitter rival, South Korea's Samsung.

Critics say Cook's team still has big questions to answer. Where, for example, are mobile payments to compete with Google Wallet, so its 800 million iTunes account holders – the largest number of credit card accounts outside a bank – can pay for things with their iPhones? Where is a smartwatch, when Samsung has released two versions since September, while Google is pushing its "Android Wear" software?

Instead, critics argue, Apple has its $3bn (£2.2bn) purchase of Beats – a company that makes headphones and offers music streaming, both of which Apple does already. "It just makes no sense," wrote analyst Pascal-Emmanuel Gobry. "This deal stinks, but more importantly it reveals that Apple as we've known and loved it is gone – for ever."

Apple's previous biggest purchase was of NeXT Computer for $400m in 1996 – a deal that brought Jobs back to lead the company.

The suggestion that Apple is wallowing in its success clearly irks the team. "Can't innovate any more, my ass," growled Phil Schiller, Apple's head of marketing as he unveiled a Star Wars-style version of the Mac Pro desktop computer.

But that was a year ago. And the pace of progress in the technology industry is relentless. In the past week alone Google and Microsoft have shown off a self-driving car and a system that translates between spoken languages in a Skype conversation.

"Apple's Beats deal is a Rorschach blot," says Benedict Evans, a partner and analyst at the venture capital company Andreessen Horowitz, referring to the psychological test where people say what they "see" in a random inkblot. "People's reactions [to the deal] slot into their existing view of whether Apple still has 'it'. If you think Apple's lost it, the Beats deal is confirmation. If you don't, it's … perplexing. This is a very out-of character move for Apple – though having everyone puzzled is in character."

Apple's top executives say they have plenty in store. Cook has promised "some exciting new products … across 2014", while Eddy Cue, who runs Apple's iTunes, Maps and iCloud divisions, said this week: "Later this year, we've got the best product pipeline that I've seen in my 25 years at Apple."

Jan Dawson, of Jackdaw Research in Provo, Utah, says the iPhone is a historical one-off because of its price ($600 wholesale) and the colossal size of the smartphone market, where 1.2bn devices will be sold this year – about two-thirds of the entire mobile phone market. Apple's entire business took off with the growth of the iPhone, he says. "There's no single product that can ever achieve those levels of revenue growth for Apple again, because nothing shares the ubiquity, subsidy and price characteristics [of the smartphone]. As such, as the iPhone growth slows, if Apple wants to achieve the same sort of growth it's achieved in the past it's going to need to do it with a large number of products rather than just one."

However, he says, "that's going to be a challenge for a company that has always prided itself on its focus on just a few great products".

But what form will new products take? And can Apple still innovate without the ferocious perfectionism of Jobs, who once called a senior Google executive on a Sunday morning because the second "O" in the Google logo on the iPhone screen didn't have the correct colour gradient. The other question is: quite what does "innovation" mean? Was the iPhone an innovation, or obvious? Was the iPad?

Professor Andrew Graves, professorial fellow of technology management at the University of Bath's school of management, said Apple's biggest risk is becoming complacent in the face of success. "I knew Steve Jobs when I was at MIT in the 1980s. He had ideas about electronic books – we all thought he was crazy. He was very good at not being complacent."

He thinks you can measure innovation – though he frets that there has been no radical innovation since the Moon landings, after centuries when breakthroughs would come every 20 years or so, from steam engines to electricity to powered flight to jet engines. "There's a dearth of companies being really innovative," says Graves, who worked in Formula One and, in the 1980s, on the concept of a driverless car as part of a Europe-funded project.

Horace Dediu, a former Nokia executive who runs the Asymco consultancy, comments: "Innovation is not a spirit. It's not some incantation or magical power. Innovation is a process involving tens of thousands of people over many years. Inspiration can influence creation, invention or novel ideas, but innovation is a system.

"Apple developed a process over a few decades and I'm doubtful that it has changed. The study of innovation is a study of systems, not people."

Academics agree. "Apple has always been known for its ability to develop business models, such as the iTunes Store, and products such as the iPod and iPhone for the mainstream market," says Bart Clarysse, chair in entrepreneurship, Imperial College Business School. "Most of these things existed before Apple turned the idea into a mainstream one. But they succeeded. Their vision was always ahead of competition and they moved into spaces nobody expected.

"This basically means that it is not technology that is the driver of this sort of innovation, but a vision on the mainstream market. Technology is an enabler, but many of the products are not technically more advanced than the competitors – on the contrary."

Cook, who joined Apple in March 1998, has always been insistent – as was Jobs – that "we're not in the junk business". Apple won't make low-cost products just to chase sales. Instead, his strategy appears to be to tempt smartphone owners using Samsung or HTC phones across to the iPhone, and then capitalise by selling apps that tie people to its platform.

Dawson at Jackdaw Research thinks that will be the way forward. "I don't buy the 'Apple has lost its mojo' stuff. But I do think success can be crippling – when you have a string of hits such as Apple has had." He thinks wearables and smart homes are "too niche" for Apple – but thinks it could make huge amounts of money through mobile payments and video services via iTunes. "It could be an enormous revenue opportunity in a space that's at least as ripe for disruption as MP3 players, smartphones or tablets were when those products launched," he said.

With iPad sales and the smartphone market slowing, Cook's biggest challenge is to demonstrate he can upset that pattern. The problem is that – as Steve Ballmer at Microsoft found before him – there's only one place you can go from being the world's largest company.