The recreational drug of choice (and availability) during both wars was tobacco. Heck, cigarettes were packaged in rations starting in WWI, and if you look at the statistics, tobacco consumption jumped during and after WWI, then exploded during WWII. By the 1950s, per-capita tobacco consumption was nearing 13 pounds per year; contrast that with about 9 pounds per year at the start of WWI.
Alternative suggestions include alcohol and caffeine, but temperance movements were only gaining strength as WWI began. In the 1914 elections, for example, "dry" laws passed in several states including Washington and Oregon. While white males of military age were among the least likely to embrace alcohol prohibition, I don't think it's appropriate to argue that alcohol was more popular than tobacco as a drug.
Caffeine, in the form of coffee, was immensely popular during WWII, but if you look at the statistics published by the U.S. Department of Agriculture (graphed here by the American Enterprise Institute), you'll see that coffee consumption actually dropped in the United States during WWI. During and after WWII, however, coffee consumption soared to the highest levels ever seen in the United States -- more than 45 gallons per capita/year. That's more than twice as much as we use even today.
Cannabis, cocaine, heroin, opium and other traditionally illegal drugs weren't in wide circulation during WWI and WWII. Their use peaked in the American military during and immediately after the Vietnam War. Even in that war, however, traditionally accepted drugs like tobacco, alcohol and caffeine remained in wider use.
I answered some questions about Amphetamine use in a previous thread.
http://www.reddit.com/r/AskHistorians/comments/22umd4/meth_use_during_ww2/
Methamphetamine was largely used by both sides, but it was most prevalent in the German and Japanese armies. The drug was distributed in large quantities to all elements of the German army, from foot-soldiers to elite troops and pilots. Between April and July 1940, Germany produced more than 35 million three-milligram doses of Pervitin (the German trademark for meth). Japan is estimated to have produced one billion Philopon (their trademark) pills between 1939 and 1945.
Meth is cheaper to synthesise than amphetamines, particularly in industrial quantities. It would have been difficult for soldiers to have been provided with cocaine in the same quantities as they were with methamphetamine, as the coca plant can only be grown in South America. The Germans did create an experimental cocktail called D-IX containing 5 mg of cocaine, 5 mg of oxycodone and 3 mg of Pervitin in each tablet. D-IX allowed Prisoners at Sachsenhausen to march 55 miles while wearing 20kg (44lb) packs. It was planned for all German troops to be supplied with D-IX pills, but the war ended before they could be mass produced.
Meth possesses both stimulant and performance-enhancing effects. Meth was provided to soldiers to lessen the toll of the mental and physical exhaustion and maintain focus. It allowed soldiers to stay awake and gave them a sense of euphoria, which was a benefit to moral.
Amphetamines were also largely used in the Second World War, often in a similar way to methamphetamine. Allied bomber pilots were provided with it to aid their focus and reduce fatigue on long missions. They could also be found in US first aid kits, for exhausted soliders.
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Depending on what you're looking for, I can recommend to you the book The Last Parallel by a Old Corps Devil Dog named Martin Russ.
The main reason I'm hesitating about posting (and would in no way be butthurt if the mods nuked this) is because the incidents depicting drug use occurred in the latter stages of the Korean War, circa 1952-1953.
The reason I'm bringing this up is because, as a former Marine Infantryman myself, I had no idea why anyone would choose to reduce their ability to fight/survive by means of....well, anything - until I read Russ's book, that is. I get doing steroids, and I've been issued stimulants - but nodding out with half a million Chinese who want to kill you less than a mile away made no sense to me.
The account of morphine and possibly heroin abuse in combat in the aforementioned book is a good micro-level look at some guys you get to know well choosing to use recreational drugs. Russ appears fairly naive about the dangers/pitfalls, but some of the other folks mentioned seem well on their way to addiction.
I hope the relative closeness of the Korean War to WWII doesn't entirely make this account useless. After all, a lot of the same guys fought in both, and a few fought in WWI, WWII, and Korea.
It was common for German a soldier in the First World War to smoke multiple cigars every day as you might imagine, particularly after a heated encounter or during the stress of heavy shelling. After such encounters alcohol was also a staple. Many German officers would drink with their men in whatever improvised quarters they had even on the eve of battle. Needless to say, they were expected to do so within reason.
Source: Ernst Jünger, Storm of Steel