"A fellow prisoner once told me he will kill my family, cut out my tongue, eyes, burn off my skin with acid and shut down my business. Well, he did kill my family. But I still have my eyes, tongue, skin. Most important: I'm still in business. Because I understood the man. So, I was ready. See, we Russians don't make threats—only promises."
The Mafia — but Russian!
OK, that's not exactly accurate.
While mobsters existed in Imperial Russia and the Soviet Union (a lot of people in The Gulag were actual criminals by objective standards), they really exploded with the collapse of the Soviet Union. There was widespread unemployment, many ex-military men and others with the right skill-set for this sort of thing, but no work. Old KGB men and lots of abandoned military hardware quickly found themselves both with new homes. Note that before The Great Politics Mess-Up, it was kinda taboo in The Mafiya to accept people who once wore uniforms and shoulderboards of any kind. After WWII, when the majority of Soviet male population (including the crooks) served in the Red Army, it even caused a major internal conflict in the gulags, called "Bitch Wars" (Сучьи войны), when the vory v zakone refused to welcome back their former peers who fought in the war. But after the USSR fell, this restriction became mostly obsolete.
Russian mobsters engage in all the activities that the Italian mobsters do. However, they are frequently depicted in a much more openly ruthless, sadistic, brutal and vicious fashion than the Italian Mafia, without the thin veneer of class and sophistication that many depictions of the Italian Mafia have built up around the organisation. This is often explained by them being tough enough to survive and prosper in the underworld of both the Soviet Union and post-collapse Russian society, neither of which were/are exactly healthy environments for milquetoasts to begin with. These days, many of the biggest Organisatsiya potentates are actually worming their way into government positions: not for nothing is The New Russia sometimes known as a "mafia state."
"Organizatsiya" ("The Organisation") is the name the Russian Mob outside of Russia use for themselves. In Russia proper, they are called "Bratva" ("The Brothers"). Members are called "tolkachi" ("pushers") or "bratki" ("bros"). There's a subtle distinction in terms:
Low-level bros may be recruited from the population of petty street Gang Bangers called gopniki (more of them below).
A bratok is a low-ranking mafiya soldier. These are stereotyped as extremely stupid and sometimes tastelessly flamboyant.
An avtoritet is a "middle manager" of the Bratva. Usually an old, crusty, experienced bro who proved to be smart enough to survive and outlive his peers.
A vor v zakone (lit. thief in law) is a high-ranking mafiya member, like an Italo "wiseguy". Traditionally, vory v zakone lived by an ascetic code of conduct that forbade having a family or large living expenses. By now, this code is a thing of the past. Another dying tradition is that because by the old proverb the prison is the home for a thief, no crook should be made without a prior conviction. Becoming a vor v zakone is a ritual that is often called "coronation" by the Mafiya members. Nowadays it's often enough to endow the "obschak"*
the underground mutual help fund-cum-expenses account
with a large sum of money to be crowned. There is no Capo-equivalent boss rank in The Mafiya. The most powerful Russian criminal masterminds are simply the older, smarter vory v zakone, with no special fancy title.
A tolkach (possibly an outdated term) is a nonviolent crook with big connections, who uses these connections to help people for a price. Unlike The Don of an Italian Mob, a tolkach doesn't directly command lesser bros, but he knows many people who do. In modern times, these people are more associated with government graft than The Mafiya proper.
A suka or ssuchenniy (literally "bitch") is any former member of the mafiya who tries to reform and aid the law. These are the enemies of any mafiya members, and that's why you should never call any Russian criminal a "bitch".
In the years following WWII, avtomatchiks (lit. "riflemen") were the crooks who fought in the war and then got back in prison for old or new crimes. The vory considered them a kind of suka because of the aforementioned taboo.
Mafiya members have a system of symbolic tattoos that reflect their position in the hierarchy and their history of crimes and prison terms. It even has symbols for "snitch" and "prison sex slave"; these are usually tattooed forcibly, as is to be expected.
During the years following the collapse of the USSR, The Mafiya was very prominent in Russian life, running many protection rackets that most small to medium businessmen had to deal with. Even now, it's far from being gone, though crooked police officers are the ones running most protection rackets now, not The Mafiya.
Something no western media and little Russian media touches upon is "Fenya" - a highly extensive thieves' cant that makes true Bratva dialogues indecipherable to civilians. Western productions have more than enough problems with regular Russian, and Russian productions would have to rely on Footnote Fever or assume viewers have extensive knowledge of the criminal world.
Note there are also Russian Gang Bangers, called gopniki. The name comes from "gop-stop" (a Fenya term for mugging) and the same "nik" suffix as in "beatnik". They are not part of The Mafiya, but rather your garden variety petty criminal youths from the Wrong Side of the Tracks, speaking badly bastardized Fenya mixed with the Russian equivalent of the Cluster F Bombs, speech spiced with a lot of "mat", practicing street robberies, vandalizing buildings and beating the crap out of gopniki from another 'hood. Some of them eventually grow into full-size bros. Some don't.
Aside from the Bratva proper, there are also ethnic mafiyas in Russia, mostly from the Caucasus. Some of them follow the usual Bratva mold, but are even more vicious and ruthless. Some (most famously the Chechen Mafiya) do not, and are even worse.
See also: Yakuza, Former Regime Personnel, The Mafia, The Triads and the Tongs, The Cartel and The Irish Mob. Often the Ruthless Foreign Gangsters in works set after 1991.
In Black Lagoon, the Mafiya is represented in Roanapur by Hotel Moscow, a group of ex-Airborne Troops led by The Baroness Balalaika. It's heavily suggested that the criminal nature of Hotel Moscow is just a front for having a large, well-trained and self-sufficient special forces unit with plausible deniability in a potentially "hot" region. Just look at Balalaika's connections!
The manga Sanctuary has them show up near the end.
Simon and Dennis from Durarara!! In their past, that is. Later volumes introduce Slon *
The Russian mob feature prominently in the action movie The Jackal where they hire the title character, a hitman to murder the First Lady, in retaliation for the death of the mob boss's brother during a joint US-Russian arrest.
Featured in Training Day where Alonzo has a debt to the Russian Mob. He doesn't pay it back in time.
A drunk chap called himself the Russian Grim Reaper in Bad Boys 2.
Playing God, starring David Duchovny, has Estonian gangsters.
In 25th Hour, Monty's associated with them, despite being of Irish descent himself.
In 2012 it is strongly implied that Curtis Jackson's Russian boss became a billionaire through less-than-legal means in one scene, although the movie never really follows up on it.
Boris the Bullet Dodger (a.k.a Boris the Blade) in Snatch is, as pedantically noted at several points, actually from Uzbekistan, but that doesn't stop pretty much everyone in the movie from thinking and speaking of him as "that sneaky fuckin' Russian." As both his previously mentioned nicknames suggest, he's pretty hard to kill.
A major antagonist in Ronin seeking the mysterious suitcase.
Antikiller interestingly portrays various strata of Russian organized crime world.
The Cindy Crawford vehicle Fair Game features an ex-KGB crime organization.
In Artemis Fowl: The Arctic Incident, Artemis is trying to rescue his father from them.
The Sterling Inheritance, by Michael Siverling, featured Uncle Gregori, who was quite kind to his nephew-in-law, even going so far as to send an arsonist to help burn down a theater for insurance when the poor nephew lost the mafiya money that he was supposed to launder to an unscrupulous Nigerian Businessman.
In one of the sequels to Gorky Park, Red Square, Renko has to deal with the Chechen Mafiya.
In Andrew Vachss' Burke book Dead and Gone, Burke meets with some Russian dudes, not too clear whether they're Bratva or gopniks, and has their tight-lipped leader assassinated so as to get in place a more talkative replacement. In Mask Market, this is subverted (!) The Russian thugs that show up are really Russian Jews.
The protagonist of All These Things I've Done, Anya, is from the Balanchine Mafiya family that manufactures illegal chocolate. The book takes place around 2083, when chocolate and caffeine are illegal and paper is hard to come by.
In Accelerando, the Mafiya of Twenty Minutes into the Future (who are all now hardcore Objectivists) have taken over the remnants of the American recording industry, which they are attempting to restore to profitability by using direct physical violence to settle intellectual property disputes.
Spooks. Lucas North, although not a member, spent eight years in a Russian prison and has a number of tattoos as a result.
The Sopranos features Mafiya as occasional antagonists of the DeMeo crime family.
An episode of Frasier revolved around him and Niles trying to get cheap, high-quality caviar from a guy with connections in the Russian Mafiya.
Roman Nabokov, shadowy nightclub owner in Life, who's turned out to be the key in the whole plot.
The Russian Mafiya features prominently in the Criminal Minds episode "Honour Among Thieves".
If the Mafiya makes an appearance on an episode of Law & Order, lots of people are probably going to die. In one of the only two-parters in the run of L&O Prime, they murdered several witnesses, killed an ADA, slashed the throat of a seven-year-old boy, and tried to blow up a police precinct. This often results in a Family Unfriendly Aesop about how, no matter how bad the regular Mafia is, at least they have rules.
In Bandit Petersburg TV series old-school, elderly criminal authority figures (think Don Vito Corleone) are juxtaposed with modern, westernized, aggressive criminal types.
In Firefly, Adelai Niska and his men are basically Russian mobsters in space.
In Dollhouse, Lubov is introduced as a low-level mobster working with the Borodins. Turns out, not so much.
In the travelogue Long Way Round, featuring Ewan McGregor and Charley Boorman, the two stars stay at the mansion of a friendly Russian man who says he's in the "washing machine business." Ewan McGregor notes with increasing unease that their host seems to know an awful lot of very large men, and has a surprisingly comprehensive personal arsenal.
Played for laughs in Delocated with Yvgeni Mirminsky, the vodka enthusiast assassin with an ambition for stand-up comedy. Then the next season they bring in his brother Sergei and things get serious.
In Cra$h & Burn the local Russian crooks are just bottom-feeding scam artists. The mob boss who comes to collect a debt from them is a high-ranking member of the Mafiya. His Dragon feels it is beneath them to handle this personally and would much rather have everyone involved killed so they can go home and get some decent food. If you try to jerk them around, they will kill you without blinking.
In Sons Of Anarchy the Russian Mafia are portrayed as being ruthless and vindictive.
Michael tries to get one of them to trust him by claiming to be one of them. He even manages to explain his obvious American accent by claiming that his family moved to the States when he was little.
Person of Interest featured a ruthless Eastern European gang that was similar to the Mafiya but was not Russian.
Season 8 of 24 has Mafiya bosses Sergei Bazhaev and Vladimir Laitanin as antagonists, as well as Davros, a more minor Mafiya member who's hired to assassinate President Omar Hassan.
In JAG, pretty much every time a storyline involves either Russians or when the main characters go to Russia, this trope almost instantly comes into play or is hinted at.
An episode of NUMB3RS dealt with a Mafiya boss who threatens Don's family in order to divert attention from his real plans, leading Don to kick Charlie off the case. It nearly works, except Charlie's brain refuses to stay off, and he eventually figures out the boss's plan, culminating in a rather complicated scheme to nab him.
Niko Bellic of Grand Theft Auto IV used to work for them, but didn't exactly part on good terms. They become the main antagonists during the game. Vlad Glebov is a low-ranked member of Bratva and Mikhail Faustin and Ray Bulgarin are vory v zakone.
Grand Theft Auto San Andreas also has C.J. and Big Smoke butting heads with Russian arms dealers in an early mission. Whether they were true bratvas or just gopniki is rather unclear. Most likely bratva, because gunrunning is usually too big and dangerous a business for gopnik gangs to organize.
Mercenaries: Playground of Destruction had them as one of the four factions with which the player could work in North Korea. Unlike the Allies, South Koreans, and Chinese, they don't have a personal stake in the conflict; they just want money, weapons, and power. The local head is an idiot Plucky Comic Relief character with a Hypercompetent Sidekick who, inevitably, gets sick of his boss and deposes him. Since they run the shop from which you purchase all your gear, it's a good idea to keep on their good side (though if you do tick them off, you can just bribe them through the website).
Vladimir Lem and his arms-dealing empire in the Max Payne series. One might consider Vlad something of a subversion of the normal Russian gangster portrayal, given that he is suave, sophisticated and friends (kinda) with the protagonist. That is, until the sequel.
The suaveness can be explained by the fact that he was Alfred Woden's protege.
Damon and Vladimir Zakarov of John Woo's Stranglehold run a Russian crime syndicate that want to take over Hong Kong.
The bandits in S.T.A.L.K.E.R. are thoroughly gopniki. Their leaders, most notably Borov, Yoga and Sultan act as typical avtoritets, though.
Russian organized criminals are sometimes mentioned in Hitman series. Arkadij Jegorov is a target in Codename 47 and Sergei Zavorotko is a Big Bad in Silent Assassin.
Alpha Protocol has contact with several elements of the Russian mafia during the Moscow mission. Sergei Surkov is an ex-vory y zakone gone semi-legit businessman (who has a lot of his ex-KGB ex-mafiya friends on payroll as security). Konstantin Brayko is a still-active gang leader and Surkov's former lieutenant who acts very much like a stereotypical bratok, what with his focus on Eighties pop culture and general lack of taste in clothing.