I know the Americans had the Glenn Miller band and Bob Hope touring around the European theater in WWII, but how far back does this practice go? And was this practice common in other countries? Were there German or Japanese musicians and comedians touring the front in WWII or further back?
I can tell you with certainty that the practice has been fairly common, at least in America, dating back to the Revolutionary War.
George Washington, encamped with the Continental Army in 1778 at Valley Forge, gave the okay for the opening of a theatre space in the camp as a way to provide relaxation for his troops after the brutal winter.
It was also used as a tool for militaristic propaganda. The play produced was Joseph Addison's 1712 Cato, a text often cited as a forebear to inspiring the revolution, and was a massive success in early Colonial American history -- in fact, it's also often cited as the source for Patrick Henry's famous "give me liberty or give me death!" It's difficult to overestimate how popular the play was.
Given the content of the play, which follows the final days of Marcus Porcius Cato Uticensis, a Roman stoic standing in resistance to Julius Caesar, and has as its central theme the struggle between individual liberty and institutional tyranny, it is not difficult to understand why Washington would have wanted the show to play for his men.
SOURCE: Bradford, William. Letter to Rachel. 14 May 1778. "Selections from the Wallace Papers." Pennsylvania Magazine of History and Biography. 40.1. (1916)