During the Bolshevik revolution, there was the communist Red Army, the Ukranian nationalist Green Army, the anarchist Black Army and the White Army. The White Army backed the Tsar and were known as the White Russians. While the drink of the same name contains a Russian spirit--vodka--it is the only tenuous link to the origin of the White Russian.
The cocktail is fairly modern, but it is definitely one of the mainstays that any bartender worth his or her salt knows how to make.
It has even made it onto the silver screen. The Dude in The Big Lebowski drank White Russians and got mighty upset when they were spilled. Catwoman in the movie of the same name ordered a White Russian sans everything but milk. Made with approximately equal parts vodka, Kahlúa and milk (or cream), this basic drink has spawned many variations (from Wikipedia with additional sources):
White Russian--Vodka, Kahlúa and milk in equal portions over ice. Tia Maria or a similar coffee liqueur can be used instead of Kahlúa. Half and half or whipping cream instead of milk can be used for a thicker concoction.
Anna Kournikova--A White Russian with skim milk; Black Russian--A White Russian sans lactose; Bolshevik (a.k.a. Blonde Russian)--A White Russian with Irish Crème liqueur instead of milk; Brown Russian--A White Russian with powdered chocolate drink mix; Cocaine Lady--A White Russian with peppermint; Dirty Russian--A White Russian with chocolate syrup; Irish Russian (a.k.a. Smooth Black Russian)--A Tall Black Russian with Guinness beer; KGB--If we told you, we'd have to kill you; Russian Yoo-Hoo--A White Russian with Yoo-Hoo instead of milk; Tall Black Russian--A Black Russian with cola; White Canadian--A White Russian with goat's milk; White Cuban--A White Russian with rum instead of vodka; White Meseta--A White Russian with a splash of bourbon; White Vegan--A White Russian with soy milk.