The "All-New, All-Different" X-Men team which debuted in 1975, was gathered from around the world. Including Wolverine from Canada, Storm from Africa, Nightcrawler from Germany, Banshee from Ireland, Sunfire from Japan, Colossus from Russia, and Thunderbird, who was Native American. They continued this trend for quite some time, with Shadowcat (Jewish), Psylocke (British), Forge (also Native American), Jubilee (Chinese-American), Gambit (Cajun... if that counts), Maggott (South Africa)... it goes on and on.
Vestiges of this were retained for the movies. Only Nightcrawler's nationality is obvious, but deleted scenes showed Storm being chased from her African village and certain details of Wolverine's uniforms (in flashback) apparently identify him as Canadian.
Also, Rogue, in the first movie, first meets Wolverine in a bar in Canada.
In First Class, Magneto practices classic Informed Judaism: We see him celebrating Hanukkah, and we see him in a Nazi concentration camp.
The X-Men spinoff book The New Mutants followed this trend. Wolfbane was Scottish, Mirage was Native American, Karma was Vietnamese, Sunspot was Brazilian and Cannonball was from the American South. Later, they added Magik from Russia, Cypher from the United States, Warlock who was an alien, and Magma who was from an offshoot of an ancient Roman tribe that lived in Brazil. Though, due to various retcons, she may be British.
Interestingly, these characters are each more complicated and "other" than their ethnic origins might suggest; the "passionate celt" Scot Wolfsbane is also religious, conflicted and repressed. The Native American Moonstar is also uncertain, suspicious, self-destructive and perhaps bisexual. The Vietnamese Karma is also (probably) a mother, later a lesbian, and prone to losses of self-control. Sunspot had an origin that cuts him off from most normal relationships; his (white, not-approved by his father) girlfriend was murdered and died in his arms, he ceases to show deep relationships after this. Cannonball joined the bad guys out of economic need, and now shows only the 'good soldier' traits expected of a good soldier.
For Moonstar, her ambiguous bisexuality might be Genius Bonus: Identifying as "heterosexual" or "homosexual" as a bifurcation is rarer on Indian reservations, largely because of a tradition of winkte, kurami, and the like. Magik also later got the Legacy Virus, which is analogous to HIV in the Marvel Universe. Wait, an ancient Roman tribe that lived in Brazil?
Generation X, New Mutants' successor title, had a multinational team, but avoided criticism of New Mutants by making their characters opposite of their ethnic stereotype (i.e. Husk, an Appalachian girl, is generally considered the brain, and Skin, who was a Hispanic gang member, is generally the nice guy, etc.).
The original Global Guardians in The DCU were a mish-mash of national stereotypes: The Knight from the U.K., Rising Sun from Japan, Tuatara from New Zealand, and so on. They got less token-ish as time went on. They made their debut in the comic adaptation of Superfriends; subtlety clearly wasn't a concern.
Justice League International was a U.N.-sponsored iteration of the famous superhero team. Most of its members were American, but Rocket Red and Captain Atom officially represented the U.S.S.R. and U.S.A. respectively, with a number of other international members as well: Fire (Brazil), Ice (Norway), Doctor Light (Japan), Crimson Fox (France), Tasmanian Devil (guess), etc.
Many of these members were taken from the pre-existing Global Guardians.
The DCnU version has Vixen (from Zambesi), August General in Iron (from China), and Godiva (from the U.K., and another former Global Guardian to boot) to the mix. And Booster Gold is now Canadian. Later additions include Batwing (Congolese) and OMAC (Cambodian)
The Club of Heroes (a.k.a. the Batmen of All Nations) from 1950s Batman comics (reintroduced in a 2008 story arc) was a loose group of non-powered heroes who were inspired by the Bat; their number included Batman (the United States), Man-of-Bats (also the United States; he was Sioux), the aforementioned Knight (Britain), the Ranger (Australia), the Gaucho (Argentina), Wingman (Sweden), the Musketeer (France), and the Legionary (Italy). The Knight, Ranger and Man-of-Bats also had Robinesque sidekicks: the Squire (who became the second Knight, and got his own Squire), the Scout (who became the Dark Ranger) and Little Raven (who became Raven Red).
Batman would later revisit the idea by creating Batman, Inc., featuring most of the above apart from the now-deceased Legionary, Ranger, and Wingman. New additions include the Hood (another representative of Britain), Mr. Unknown (Japan), and Nightrunner (France, replacing the retired Musketeer). There's also Batwing (Congolese), and a mysterious new Wingman (who turned out to be the American Jason Todd). Batman, Inc. might not seem like much of a team, but they operate independently and come together to tackle greater crises — like the Justice League.
Green Arrow, at the time practically a same-company Captain Ersatz of Batman, had his own Club of Heroes. "The Costumed Archers of the World" included the Ace Archer (Japan), the Bowman of the Bush (Australia), the Phantom (France), the Bowman of Britain (Britain) and the Archer of Arabia (Saudi Arabia), in addition to the American Green Arrow.
The Blackhawk Squadron that existed between 1941 and 1983 consisted of: Blackhawk (aka, sometimes, Bart Hawk — Polish, American, or Polish-American, Depending on the Writer); André Blanc Dumont (France); Olaf Bjornson (Norway... or possibly Sweden); Chuck Wilson (USA, specifically Texas); Hans Hendrickson (Netherlands); Stanislaus (Poland); Chop-Chop (aka Liu Huang or Wu Cheng, China); Zinda "Lady Blackhawk" Blake (USA).
In a 1987 miniseries, Howard Chaykin introduced an updated, slightly different, version of the team, which carried over into a subsequent ongoing series. These Blackhawks included: Janos "Blackhawk" Prohaska and Stanislaus Drozdowski (Poland); André Blanc-Dumont (France); Olaf Friedriksen (Denmark); Carlo "Chuck" Sirianni (Italy by way of the United States); Ritter Hendricksen (Netherlands); Weng "Chop-Chop" Chan (China); Natalie "the other Lady Blackhawk" Reed, and Grover Baines (the United States); Quan Chee Keng (Malaysia); and Paco Herrera (Mexico).
The modern incarnation of the team seemed to follow suit to some degree; the nationalities of Andrew "Blackhawk" Lincoln, Lady Blackhawk, and Randall Wildman were never revealed (though Lincoln is likely American), but Kunoichi is Japanese, Canada is American (Nicknamed after an incident in a bar in Calgary), the Irishman is Ukranian (but born to American parents; he got his nickname from fellow Spetsnaz operatives due to his red hair), and Attila is Hungarian.
The Apollo Eleven from Astro City were a team of astronauts from around the world sent to man the first moonbase; something up there changed them into superhumans and they came back with an eleventh person.
The Suicide Squad has included at various points Captain Boomerang (both of them; Australian), Stalnoivolk (Russian), Ravan and Rustam (Quraci), Plastique (Quebecoise), Count Vertigo (Vlativan), Manchester Black and the Shade (English), Javelin (German), Mirror Master (Scottish), and virtually everyone else is American.
Marvel's Circus of Crime is surprisingly cosmopolitan, featuring the Ringmaster (Austrian), Bruto the Strongman (Swedish), Fire-Eater (Spanish), the Great Gambonnos (Italian), Rajah (Indian). The Human Cannonball, the Clown, Live Wire, Princess Python, and Blackwing are Americans.
Jack Kirby's Boy Commandos: Dan "Brooklyn" Turpin (US), Alfie Twigett (UK), André Chavard (France) and Jan Haasan (Netherlands).
The titular team in The Boys: the leader and the viewpoint character are British, and there's also a Frenchman and two Americans.
The latest incarnation of Image Comics' Guardians of the Globe features Bulletproof, Black Samson, Knockout, and Brit (American), Kid Thor (Canadian), the Yeti (Nepalese), Kaboomerang (Australian), Outrun (South African), El Chupacabra (Mexican), Best Tiger (Chinese), Cast Iron (From an unspecified former Yugoslav state), Pegasus (Russian), Japandroid (Japanese), Le Bruiser (French), and Shapesmith (Martian). Recruiting heroes from all over the world was a deliberate move on team coordinator Cecil's part — they're guarding the globe, and everyone should have a part in it.
The Avengers, much like the JLA, have also had many international members as well as non-humans, although they are usually sponsored by the US government.
The original Stormwatch team consisted of Battalion (American), Fuji (Japanese), Hellstrike (Irish), Winter (Russian), and Diva (Italian). They were joined in short order by Flashpoint (Australian), Sunburst (Swedish), Nautika (not human, origin unspecified), Flint (Kenyan), and three additional Americans in Synergy, Cannon, and Fahrenheit. One of the team's names in development was "Multinational Force", with the designs of the original team members having their nations' flags painted on their faces. Fuji's design was notably unchanged from this phase.
Flint was introduced as part of a short-lived "new" Stormwatch team consisting of herself, the Canadian Blademaster, the Tibetan Swift, and the Native American Comanche.
The version of The Authority backed by the G7 featured members from each of the world's seven richest nations: The Colonel from Britain, Street from the United States, Teuton from Germany, Rush from Canada, Last Call from Italy, the Surgeon from France, and Machine from Japan.
The Authority themselves were originally led by a Brit and included a Tibetan (Swift) and a Netherlander (The Doctor) along with whatever nationality Apollo and Midnighter possessed before losing their original identities, and the second Doctor was a Palestinian.
Excalibur basically acts as a cross between the X-Men/Avengers for Europe. In its initial incarnation it had Captain Britain (just guess...), Meggan (British/Fey), Nightcrawler (German), Shadowcat (American/Jewish), Lockheed (alien dragon) and Phoenix (Alt. Future America). In time the lineup changed and at one point or another also included Colossus (Russian), Douglock (alien, different race), Wolfsbane (Scottish), Widget (extradimensional robot), Black Knight (American), Feron (Fey/alternate universe), Cerise (yet another alien race), etc.
The modern incarnation of the Green Team had Commodore Murphy (British), JP Houston (American; Texan), Cecilia Sunbeam (American; Californian), and Prince Mohammed Qahtanii (from some fake Middle-Eastern country).
The Hand of the Morningstar has Titan (American), Avatar (Indian), Shango (West African), Kwan Yin (Chinese), and Kami (South American).