Depends on what you mean by "effective". Laws limiting access to alcohol, including prohibition, definitely reduced alcohol consumption and led to reduced cirrhosis rates in the US and (during Canada's prohibition period) in Canada. It did not eliminate consumption, and it had a lot of unintended consequences.

Legal prohibition in the US was passed at a federal level in 1920 and repealed in 1933, but there were numerous statutes in the years leading up to 1920 that limited the sale and distribution of alcohol. While reported consumption dropped during this period, this is reasonably thought to be a result of reluctance to self-report on illegal activity. Instead, we can use liver cirrhosis death rates, which track alcohol consumption levels reasonably closely on an national and international level, as a measure of alcohol consumption.

During the US prohibition, deaths due to liver cirrhosis were notably lower, but as you'll notice from the graph, cirrhosis death rates dropped prior to 1920 and did not rebound immediately upon repeal. The decline in cirrhosis before 1920 may be linked in part to the fact that 35 states enacted prohibition in the years prior to 1920, although state-level prohibition has a weak association with cirrhosis rates. Federal laws prior to prohibition are more likely candidates for explaining the drop, including higher tax rates, the 1917 Reed bone-dry law, and laws in 1918-1919 that closed distilleries and breweries. The fact that cirrhosis death rates did not rise immediately after prohibition ended might be due in part to the fact that drinking rates are expected to lag behind cirrhosis deaths by a number of years. When these factors are accounted for, prohibition is linked to a 10-20% drop in cirrhosis rates due to a reduction in alcohol consumption. Most information above from Dills and Miron 2003, "Alcohol Prohibition and Cirrhosis."

Canada experienced a similar pattern, with nationwide alcohol prohibition in 1918-1920 and with laws restricting or prohibiting alcohol varying by year and by province both before and after this period. These efforts were linked with a statistically significant reduction in cirrhosis deaths as well.

I won't get into the unintended consequences and costs (both financial and social) of prohibition, but it is false to claim that these laws were completely ineffective.

Edit: Statutes, not statues, darn it.

Alcohol had been regulated during WWI for the first time in many countries, due to wartime and industrial restrictions as well as growing temperance movements. While this confluence led to prohibition in the US, in other places Alcohol remained legal but much more stringent regulations were put in place following WWI.

US national alcohol consumption is believed to have declined 30-40% in the early years of prohibition before recovering to per-prohibition levels.

The regulatory approach seems to have been more effective, in the United Kingdom national alcohol consumption decreased by 50-60% from a much higher per-capita rate. The UK reductions also lasted for several decades rather than several years, until alcohol regulations were ultimately relaxed.

A similar effect is seen in the reductions in US tobacco consumption through regulation (per-capita consumption has declined 60% since 1963), which dwarf the reductions achieved for illicit narcotics through prohibition.

Prohibition likely decreased US alcohol consumption only in the short term. It was also ineffective in comparison to the regulatory approach pursued by other countries such as the UK. Prohibition also drove a considerable degree of criminality, while depriving the US government of considerable tax revenues offered by alternative policies.

Reasons for failure

Prohibitionist Narcotics policy has two elements:

1. Supply control: In which the state targets the producers, smugglers, and retailers of illicit narcotics
2. Demand control: In which government policies attempt to reduce consumer demand through addiction treatment, consumer education, and treating the underlying social problems associated with addiction

Supply control can produce only modest reductions in narcotics consumption, the financial incentives and the size of the market (particularly for alcohol) make it economically impossible for the state to eradicate illicit narcotics. Short terms gains and major drug busts increase prices and further inflate the incentives for people to participate in the production/distribution of the narcotics. So any short term reduction in narcotics supply drives long term increases in supply. The war on drugs is, in this sense, a war against basic principles of supply and demand.

What is more, research indicates that every dollar spent on addiction treatment produces an decrease in narcotics consumption equivalent to $23 spent on source-country control, or $7 of domestic enforcement. So demand control is much more effective, and can take place whether a particular narcotic is legal or illegal.

The regulation of legalized narcotics also offers considerable additional advantages over prohibition:

• Restrictions such as limited hours (alcohol can only be sold between noon-8pm for example) have a nudge effect on consumption while not being onerous enough to provoke illicit retail.
• Strict licensing schemes for liquor stores or bars can make them partners in state efforts to reduce consumption. While a speakeasy has no incentive to serve clients in moderation, a bar which can lose its license for over-serving is motivated to restrict excessive consumption by clients.
• Legal regulation also allows the state to impose excise taxes or minimum prices, generating tax revenue which can be spent on addiction treatment. The resulting price increases also decrease narcotics consumption.
• Regulation can also shift the culture of consumption. Whereas prohibition caused consumers to increasingly consume hard liquor rather than beer or wine. Licensing laws and regulatory rules pushed pubs in the UK to be required to serve food with alcohol, to make their premises more family friendly, and shifted the drinking culture of the UK in the opposite direction to the US.
• Legalization also allows government resources to be shifted from policing and interdiction to treatment and other social programs which more effectively reduce narcotics consumption.

Prohibition failed because the massive financial incentives for bootleggers cannot be overcome through policing alone, even if your entire national GDP is spent on demand control and policing. Prohibition also failed because prohibition is a less-effective means of reducing both alcohol addiction and alcohol consumption than many alternative regulatory policies.

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Sources:

• Dills, Angela K., and Jeffrey A. Miron. "Alcohol prohibition and cirrhosis." American Law and Economics Review 6.2 (2004): 285-318.
• Gourvish, Terence R. "The Business of Alcohol in the US and the UK: UK Regulation and Drinking Habits, 1914—39." Business and Economic History (1997): 609-616.
• MacCoun, Robert J., and Peter Reuter. "Assessing drug prohibition and its alternatives: A guide for agnostics." Annual Review of Law and Social Science 7 (2011): 61-78.
• Rydell, C. Peter, S. M. Everingham, and Susan S. Everingham. Controlling cocaine: Supply versus demand programs. Vol. 331. Rand Corporation, 1994.