The USA had her Wild West. Russia, on the other hand, got her Wild East. Two dangerous frontiers where only the toughest could survive. So far, we know a lot about cowboys, both facts and popular misconceptions that created tropes and fashions. Do Russians have an equivalent of their own? You know, Wyatt Earp, Doc Holliday, Bass Reeves, Billy the Kid and the likes?
I am no student of late Russian folklore (ask me about Baba Yaga...), but just by virtue of living here and holding a degree in history (and years of journalistic experience)...I would say two related things loosely qualify. One is the heroes of the Russian Civil War, such as Vasily Chapayev or Grigory Kotovsky, maybe Marshal Budyonny too. They were enshrined in the Bolshevik/Communist historical canon, there were books and movies about their fights, the 1934 “Chapayev” film being a classic here for quite a while. Granted, the myth gradually became fuzzy, and such folks themselves are now not so much action heroes as vague figures out of a dusty legend; I doubt many people under 40 would be able to name a single heroic exploit by Kotovsky, while Chapayev devolved into a staple subject of various jokes (most of them untranslatable and/or terrible).
However - and this is probably more relevant to your question - there is also quite a tradition of a film genre called “Ostern”, or “Eastern”. Wiki actually covers the topic quite well, but I can confirm from personal experience that such films, also usually set in/around the Civil War and depicting fights between brave Bolsheviks with guns and lawless bandits or the Whites, are popular and well-known to this day. “The White Sun of the Desert” (1969) is probably the best example of the genre, with an imperturbable Red Army rifleman, Comrade Sukhov, bringing down a gang of Basmachi in the Caspian desert, though “The Elusive Avengers” (1966) is a close contender. All these movies remain known and popular - to the extent where all ISS expeditions from Baikonur are actually tradition-bound to watch “The White Sun” before launch.
There is no, or little, such stuff produced in post-Soviet times, however. The explanation to that would fall under the 20-year rule, and so I’ll just put it down to Russia’s ongoing struggle to reconcile/choose between its pre-Soviet and Soviet historical myths. Interestingly, there are also no such gunslinger stories from pre-Soviet times, even though things like the conquest of Siberia and Central Asia offer plenty of opportunities. I would pin it down to the Soviet propaganda not being keen on extolling the virtues of those Tsarist imperialists, and so whatever tradition they might have had before 1917 died or never took the jump to modern pop culture.
TL;DR: yes, mainly centered around the Russian Civil War. Including some historic figures and some fictional Clint Eastwood equivalents with a Red Star badge.
/u/poob1x compares the Russian Far East to the American West.