What is the elephant in all our rooms? It is the global triumph of capitalism. Democracy is fiercely disputed. Freedom is under threat even in old-established democracies such as Britain. Western supremacy is on the skids. But everyone does capitalism. Americans and Europeans do it. Indians do it. Russian oligarchs and Saudi princes do it. Even Chinese communists do it. And now the members of Israel's oldest kibbutz, that last best hope of egalitarian socialism, have voted to introduce variable salaries based on individual performance. Karl Marx would be turning in his grave. Or perhaps not, since some of his writings eerily foreshadowed our era of globalised capitalism. His prescription failed but his description was prescient.

Here is the great fact about the early 21st century, so big and taken for granted that we rarely stop to think how extraordinary it is. It was not ever thus. "Can capitalism survive?" asked the British socialist thinker GDH Cole, in a book published in 1938 under the title Socialism in Evolution. His answer was no. Socialism would succeed it. Most readers of this newspaper in 1938 would probably have agreed.

What are the big ideological alternatives being proposed today? Hugo Chávez's "21st century socialism" still looks like a local or at most a regional phenomenon, best practised in oil-rich states. Islamism, sometimes billed as democratic capitalism's great competitor in a new ideological struggle, does not offer an alternative economic system (aside from the peculiarities of Islamic finance) and anyway does not appeal beyond the Muslim umma. Most anti-globalists, altermondialistes and, indeed, green activists, are much better at pointing out the failings of global capitalism than they are at suggesting systemic alternatives. "Capitalism should be replaced by something nicer," read a placard at a May Day demonstration in London a few years back.

Of course there's a problem of definition here. Is what Russian or Chinese state-owned companies do really capitalism? Isn't private ownership the essence of capitalism? One of America's leading academic experts on capitalism, Edmund Phelps of Columbia University, has an even more restrictive definition. For him, what we have in much of continental Europe, with multiple stakeholders, is not capitalism but corporatism. Capitalism, he says, is "an economic system in which private capital is relatively free to innovate and invest without permission from the state, green lights from communities and regions, from workers, and other so-called social partners". In which case most of the world is not capitalist. I find this much too restrictive. Surely what we have across Europe are multiple varieties of capitalism, from more liberal market economies like Britain and Ireland to more coordinated stakeholder economies like Germany and Austria.

In Russia and China, there's a spectrum from state to private ownership. Other considerations than maximising profit play a large part in the decision-making of state-controlled companies, but they too operate as players in national and international markets and increasingly they also speak the language of global capitalism. At this year's World Economic Forum in Davos, I heard Gazprom's Alexander Medvedev defend the company's record by saying that it is one of the world's top five in market capitalisation and constantly looking for value for its shareholders - who happen to include the Russian state. At the very least, this suggests a hegemony of the discourse of global capitalism. China's "Leninist capitalism" is a very big borderline case, but the crab-like movement of its companies towards what we would recognise as more rather than less capitalist behaviour is far clearer than any movement of its state towards democracy.

Does this lack of any clear ideological alternative mean that capitalism is secure for years to come? Far from it. With the unprecedented triumph of globalised capitalism over the last two decades come new threats to its own future. They are not precisely the famous "contradictions" that Marx identified, but they may be even bigger. For a start, the history of capitalism over the last hundred years hardly supports the view that it is an automatically self-correcting system. As George Soros (who should know) points out, global markets are now more than ever constantly out of equilibrium - and teetering on the edge of a larger disequilibrium. Again and again, it has needed the visible hands of political, fiscal and legal correction to complement the invisible hand of the market. The bigger it gets, the harder it can fall.

An oil tanker is more stable than a sailing dinghy, but if the tanker's internal bulkheads are breached and the oil starts swilling from side to side in a storm, you have the makings of a major disaster. Increasingly, the world's capital is like oil in the hold of one giant tanker, with ever fewer internal bulkheads to stop it swilling around.

Then there is inequality. One feature of globalised capitalism seems to be that it rewards its high performers disproportionately, not just in the City of London but also in Shanghai, Moscow and Mumbai. What will be the political effects of having a small group of super-rich people in countries where the majority are still super-poor? In more developed economies, such as Britain and America, a reasonably well-off middle-class with a slowly improving personal standard of living may be less bothered by a small group of the super-rich - whose antics also provide them with a regular diet of tabloid-style entertainment. But if a lot of middle-class people begin to feel they are personally losing out to the same process of globalisation that is making those few fund managers stinking rich, while at the same time outsourcing their own middle-class jobs to India, then you may have a backlash. Watch Lou Dobbs on CNN for a taste of the populist and protectionist rhetoric to come.

Above all, though, there is the inescapable dilemma that this planet cannot sustain six-and-a-half billion people living like today's middle-class consumers in its rich north. In just a few decades, we would use up the fossil fuels that took some 400 million years to accrete - and change the earth's climate as a result. Sustainability may be a grey and boring word, but it is the biggest single challenge to global capitalism today. However ingenious modern capitalists are at finding alternative technologies - and they will be very ingenious - somewhere down the line this is going to mean richer consumers settling for less rather than more.

Marx thought capitalism would have a problem finding consumers for the goods that improving techniques of production enabled it to churn out. Instead, it has become expert in a new branch of manufacturing: the manufacture of desires. The genius of contemporary capitalism is not simply that it gives consumers what they want but that it makes them want what it has to give. It's that core logic of ever-expanding desires that is unsustainable on a global scale. But are we prepared to abandon it? We may be happy to insulate our lofts, recycle our newspapers and cycle to work, but are we ready to settle for less so others can have more? Am I? Are you?

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