I read the answer about the German Imperial Army in WW1 in this thread:
How common was it that soldiers were given cigarettes in their rations? Why?
It was extremely common. The British army ration included an allowance of up to 2 ounces of tobacco per man per week. At the outset of the war pipes were the most common method of smoking, but pre-packaged cigarettes rapidly gained popularity as they were much more convenient in trench conditions. I've mentioned a little about brands and prices in this answer:
What was the most popular method of smoking tobacco in Europe just after WWI?
Soldiers would often supplement their ration with privately-purchased tobacco for two reasons. Firstly, the ration wasn't enough for a heavy smoker, especially given that chain-smoking in moments of boredom and terror at the front was common. The supply was never guaranteed and prone to disruption - there was often trouble enough getting food and water into the line - although at times there could be a glut (rations were issued by the QM based on the reported strength of the previous day, so casualties meant bonus food and other supplies for survivors). Secondly, Government-issue tobacco was frequently awful, so soldiers would purchase better brands from canteens and estaminets when they had the chance, or ask for them to be sent from home by relatives:
‘What are the cigs? Any Woodies?’ Woodbines were always prized above other brands. White Cloud and other brands were hated because their green tobacco had a revolting, acrid taste and we suspected they’d been foisted on the government by fat profiteers who, we believed, smoked cigars themselves.
From Tales of the Old Soldiers by Tom Quinn, (Stroud, 1993) p63
Dried fruit such as raisins were also given out with rations; you would get a handful and put them in your pocket and eat them like sweets. Men who didn't smoke could swap their cigarettes for more raisins; indeed you could swap cigarettes for a great many things, and they became a kind of currency in the trenches.
At Christmas 1914 the Princess Mary Gift Fund Box was widely issued to British and Empire troops, with tobacco and cigarettes being the main contents in most.
As to the why, I think the answer by /u/ozminer covers it well: they were a morale booster and a useful distraction, and smoking was simply extremely common at the time. And more practically, if men addicted to nicotine were deprived of it then mood, morale, and discipline would suffer.
In almost every army you were given cigarettes, it kept the men happy and boosted morale. Cigarettes are a stimulant and a appetite suppresser, keeping them less hungry and awake.