Ruthless Foreign Gangsters

A common reason for a Mob War is an outsider faction, usually a Triad or The Mafiya attempting to gain foothold on new ground, stepping on the foot of a local gang. In these cases, the invading new criminals are generally seen as more ruthless and prone to break the local's code of honour.

The grain of Truth in Television, of course, is that organized criminal families that want to get from day to day in a community have to maintain public relations, and thus on home ground cannot play as dirty as elsewhere.

During the 1980s The Cartel would be a popular candidate, after the Soviet Union collapsed, Organizatsiya and their east block cousins took the role.

See also Mob War. Sometimes the moral is that Our Criminals Are Better. When the Foreign Gangsters aren't particularly worse than the home-turf ones, they're just a Generic Ethnic Crime Gang.

Examples of Ruthless Foreign Gangsters include:

Anime & Manga

Hotel Moscow in Black Lagoon when Balalaika is called in to consolidate a foothold in Japan through an alliance with a local Yakuza clan (and, like the Magnificent Bitch she is, doing just that).

The hometown of the cast, Roanapur, is usually an inversion of this trope—the town is such a Wretched Hive that it's hard to find anyone more ruthless than its normal citizenry moving in. When the Florida cartel tries to make a move within the city they're mostly treated like Harmless Villains by the resident gangster community.

Comic Books

Spider-Man - Subverted with Black Tarantula, a crime lord from Argentina trying to expand his empire to the States, starting with New York. He's almost a saint compared to other marvel villains however. In later Daredevil comics he convinces people he's reformed and even after turning on Daredevil, uses his powers to heal him after he getting his money, oh he leaves Daredevil some of the money saying help somebody with it!
The Punisher MAX - One of the most horrifically brutal versions pops up here, naturally, in "The Slavers" story arc. The titular criminals are a group of ex-military from East Europe who bring a human trafficking ring into New York, and fall under Frank Castle's personal attention. Notably, this gang is so vicious and horrible that they earn a dubious distinction:

Castle: It was in that moment that I realized something. A dull, blurred feeling that I’d had since this whole mess began, all of a sudden crystal clear. It had been a long, long time since I hated anyone the way I hated them.

- Oddly reinforced in how they hold the distinction of being the only group to "beat" Frank Castle in a gunfight (read: forcing Frank Castle to flee for his life) when Garth Ennis was writing the 2004-2008 run.
Sin City features a German mob boss named Herr Wallenquist.

Film

The Italian Job: The Ukrainian mob is so ruthless, even the Korean mob won't mess with it.
Layer Cake, with the Neo-Nazis in the book and Serbians in the movie. Particularly the latter, where the foreign mob is much more violent, but also has a keen sense of honor. The Serbians don't actually care about the money but about maintaining their reputation as Ruthless Foreign Gangsters.
Taken is set in France, with Albanians as the villains.
In the Brandon Lee vehicle Rapid Fire, the previous Big Bad is executed in his jail cell by the men of an Asian crime lord about midway through the movie after getting his ass kicked by the hero. The crimelord then becomes the new Big Bad.
In The Long Good Friday, East End mob boss Harold Shand tries to make a property deal with the American mafia, but suddenly all his men start getting bombed. Shand eventually realizes that he's somehow incurred the wrath of the IRA. Everyone tells him that the IRA is too psychotic to fight, but he tries to out-muscle them. It doesn't go well for him. Interestingly, the Mafiosi are portrayed as simple businessmen who don't want any bloodshed getting in the way of a deal.
Punisher (1989) - The Yakuza take on this role with respect to The Mafia.
Training Day has an unnamed Russian crime group that is out for Alonzo's head after he killed one of their people in Las Vegas. Even though Alonzo is a corrupt cop with a lot of power in the underworld, he needs to get lot of money to pay them off, or they'll kill him.
In Pusher, Frank incurs debt to Milo, a ruthless Serbian drug lord in Denmark. In the third film, Milo runs afoul of even more ruthless Albanians.
The French gang boss in Bad Boys who's plan seems to revolve around killing every single person he comes into contact with.
Cradle To The Grave has arms dealers from Taiwan take out the local thugs.

Literature

Inverted in Tamora Pierce's Terrier and Bloodhound; where Beka spends most of her time taking out the Ruthless Local Gangsters, while dealing with (relatively) Family Friendly Foreign Gangsters (Rosto the Piper and his friends).
In Red Square, a book in the Arkady Renko series, it is discussed how since the fall of the Soviet Union that there are now Chechen Mafiya members in Germany. Germany is still trying to figure out how to react to them, as they don't follow the normal German constraints and are openly brutal.

Live Action TV

The Sopranos - Tony's crew versus Eastern Europeans.
The Shield - The Armenian Mob. With the Mexicans, the El Salvadorians, and even the Koreans trying show them up. Frankly, if you're an immigrant minority without a ruthless gang to show for it, you get stepped on. Also somewhat subverted in that the black gangs, who used to play the Ruthless Gangster role, are now the established ones with some standards.
In Deadwood, a Triad gang under the employ of George Hearst tries to muscle into Deadwood and push out the local Chinese strongman, Mr. Wu. Al Swearengen convinces Hearst to swap his support to Wu, and the Triads are slaughtered.
In the Numb3rs episode "Backscatter", the Eppes family is targeted by the Russian Mob.
In Justified a Colombian drug cartel operating out of Miami ships its drugs through Harlan County, Kentucky and do not want to pay Bo Crowder for 'protecting' their shipments so they arrange for him to be arrested and sent to jail. However, they are content to stay out of Harlan County unless someone there interferes with their business.
- In season 3 Quarles, a mobster from Detroit, tries to setup a major drug operation in Harlan County and makes the mistake of trying to muscle out Boyd Crowder. Although Quarles is extremely ruthless and deadly, his lack of understanding how things in Harlan County really work dooms him to failure.
In Season 2 of Intelligence, the ruthless foreign gangsters are Americans looking to take over the Vancouver drug trade. The protagonist spends the latter half of the season trying to organize all of the city's rival gangs into a syndicate to freeze the Americans out.

Video Games

Common plot in the Grand Theft Auto series since Grand Theft Auto III. In San Andreas, the Da Nang Boys are a ruthless Vietnamese gang stepping on the Mountain Cloud Boys' toes. Later, The Triad plays this role against The Mafia families in Las Venturas. Although the protagonist is helping the Triads, and they get pictured slightly nicer than the regular Mafia.

In Grand Theft Auto IV you arguably play as one of these characters. But you also do deals and missions for "traditional" biker gangs and Italian mobsters as well.

The plot of the John Woo game Stranglehold initially sets things up like this, with the Golden Kane allying with a ruthless Russian syndicate against the Dragon Claw syndicate headed by Mr. James Wong. But in a subversion of this trope, as Tequila and the audience find out, Wong is not a Neighborhood Friendly Gangster, and is even worse than the other bosses put together, particularly when he crosses the Moral Event Horizon and has his own daughter murdered by Tequila's partner.
In Yakuza 2, not only does Kiryu have to fight Sengoku and his band of rival yakuza, he also has to deal with some ruthless Korean gangsters led by Kim Taejin, a.k.a. Terada Yukio, the guy who you placed in charge of your syndicate at the very end of the first game.
In the original Mercenaries, the player dealt with the Russian Mafia, who, in exchange for some odd jobs, would allow the player access to their black market online storefront, the Merchant of Menace; they were really the only source for ordering weapon kits and airstrikes in the field. In the sequel, the Jamaican Pirates also sell gear, but are much less relevant to the plot or critical to your success. For some reason, both had a version of s skull and crossbones as a faction logo.
In Neverwinter Nights 2, a less-than-lawful Player Character can get involved in a mob war between Luskan gangs trying to establish a hold in Neverwinter and the Shadow Thieves of Amn, who have an established operation in Neverwinter.
Inverted in Final Fantasy Tactics A2: Although Duelhorn, the invading gang, still forces local clans to work for them and can be rather violent, three of their four leaders are Anti Villains and treat their members nicely. Khamja, the local gang, is far more secretive, dishonest, and ruthless even to their own members.
Inverted and played with in in The Elder Scrolls III: Morrowind. The Thieves' Guild is significantly less brutal than their native counterpart in the Camonna Tong. The Dark Brotherhood/Morag Tong is... muddled. The Dark Brotherhood is more foreign-ish, and more ruthless, but the foreignness has more to do with the Morag Tong being official than the Dark Brotherhood actually being new to the area and foreign.

Web Comics

Order of the Stick has a fantastic variation.