After totaling all spending, a study by Kevin Murphy, Steve Cicala, and
myself estimates that the war on drugs is costing the US one way or
another well over $100 billion per year. These estimates do not include
important intangible costs, such as the destructive effects on many
inner city neighborhoods, the use of the American military to fight
drug lords and farmers in Colombia and other nations, or the corrupting
influence of drugs on many governments.
The best economics piece on this issue is Drug War Crimes a short book by Jeffrey Miron published by Independent Institute where I am the director of research. Miron demonstrates that the war on drugs greatly increases the violent crime rate (just as it rose during alcohol prohibition) and that the policy is not very effective in reducing consumption.
One interesting reason why the drug war reduces consumption less than people imagine is that prohibition reduces some costs. Drug sellers, for example, do not pay social security taxes for their employees, they do not follow minimum wage laws and they do not obey costly FDA regulations. On net prices are still pushed up by the threat of prosecution but the lack of taxes and regulations is a countervailing factor.