"Drug use is not down. It's time for a different approach. Drugs have destroyed many people, and the wrong government and policies have destroyed many people."

"It has been a disaster and has inflicted enormous harm," Annan, who is currently chair of The Elders, a group of world leaders, told the World Economic Forum in Davos.

The decades-long war on drugs has failed and the world's lawmakers need to consider decriminalization, influential world leaders including ex-United Nations Secretary General Kofi Annan and the President of Colombia have said.

(Read more: Making the case for marijuana legislation)

After a number of countries and U.S. states such as Colorado softened their attitude towards illegal drugs, the issue has moved further to the front of the global agenda. Illegal drugs have become cheaper and purer in recent years, as drug cartels get more efficient, according to a study by the International Centre for Science in Drug Policy late last year.

There is a difference between full legalization and decriminalization, where substances are still subject to some restrictions of use.

Rick Perry, the governor of Texas who made an abortive run for the Republican Presidential nomination, argued against decriminalization.

"It's bad public policy for government to say: 'Here's one more substance that's not good for you that's legal," he said.

(Read more: Colorado's brand-new pot economy)

If drugs were endorsed by "influential men and women" this might have an impact on easily influenced youth, Perry argued.

"My country has suffered probably the most from the war on drugs. We need to find more efficient ways to combat it," Juan Manuel Santos, president of Colombia, told CNBC.

"How can I tell someone with half a hectare growing marijuana, that he has to go to jail?"

The next meeting of the United Nations Commission on Narcotic Drugs, in Vienna in March, could be a key turning point in the change on international drugs policy, according to Santos.

Tracking down bankers who help funnel cartels' money is really key, according to Perry. He highlighted the success of drugs courts in Texas.

The war on drugs has imprisoned a disproportionate number of black people in the U.S., its critics point out.

"People are being given enormous prison terms just for use. There has got to be a better way than ruining so many people's lives," Kenneth Roth, executive director of Human Rights Watch, said.

- By CNBC's Catherine Boyle. Twitter: @cboylecnbc.