The only teams that exist in any North American sports league are based in New York, Los Angeles, Washington, San Francisco, Chicago, Detroit, Denver, Boston, Atlanta, Miami, Houston, St. Louis, Seattle, the Twin Cities, and Philadelphia. Teams in places like Milwaukee, Kansas City, Nashville, or any of the Canadian NHL teams (except Toronto and Montreal) don't exist.
However, everyone knows Wisconsin has an NFL team, considering their sports rivalries, colors, the distinctive hats worn by theirs fans, and the town they are based in.
Even with the NHL, a lot of people recognize the Montreal Canadiens's logo as having something to do with hockey, but have no idea what specifically. If an American source is aware of that team at all, they will often misspell their name "Canadians" (i.e. assume the English, rather than the French, spelling applies). With the exception of the NHL teams (and it's not like hockey is a real sport, anyways), this is somewhat Truth in Television, at least as far as the championships go.
No U.S. city south of Washington D.C. or west of St. Louis has an NHL team, with the possible exception of LA (especially when Gretzky played for them).
Any English football (soccer) game will be played between Team X and Manchester United, where Team X is either Liverpool or maybe Arsenal. (Probably doesn't apply in England).
New Yorkers going to a hockey game will only ever see the New York Rangers, even if attending an Islanders' game on Long Island or a Devils' game in New Jersey would be more convenient or accessible.
The only hockey player to have ever existed in the past 25 years is Wayne Gretzky. But then, he was the "Great One" (a nickname most people have forgotten originally belonged to Jackie Gleason).
Outside the U.S.A., Babe Ruth will be the only baseball player some people might have heard of. Or Jackie Robinson, because he's black.
In the entire world, Pélé and Diego Maradona are the most well known soccer players. In more recent times, David Beckham will be the name even non-sport fans have heard about.
Zinedine Zidane is the only French player, and he only deserves to be known because of a certain incident involving some Italian guy.
If a boxer has to be named it will be Muhammad Ali or Mike Tyson. Only a few people have ever set foot in an American boxing arena: Mike Tyson, Muhammad Ali, George Foreman, and Evander Holyfield. If a boxer isn't American, they'll be drawn from a pool of about two from a given country.
If a cyclist has to be named, it will be Eddy Merckx or in the U.S.A., Lance Armstrong.
Chess players? Gary Kasparov, Anatoly Karpov, and Bobby Fischer.
Athletes? Jesse Owens or, in more recent times, Usain Bolt. The British might namedrop Roger Bannister.
Tennis players will usually be the champions like Bjorn Borg or Venus and Serena Williams. In the 1970s and 1980s, John McEnroe will be referenced a lot as well, due to his bad behavior on the court. In the early 2000s, Anna Kournikova was well known, but mostly for her looks. (As for that "other" Anna Kournikova, you're thinking of Maria Sharapova.)
In the UK, they will be considered ultimate failures if they never won Wimbledon — no matter how many other Slams they won. Conversely, someone like Pat Cash (who won the title in 1985 with a one-off inspired performance) can make a second career as a BBC pundit forever on the basis of that one Slam.
Roger Federer and Rafael Nadal are often the only male tennis players non-tennis fans can name off the top of their head in The New Tens, to the point where a fair number of them express shock when they're told that the current No. 1 player is actually neither of them (Novak Djokovic, as of this time of typing).
In the early 20th century, Johnny Weissmuller will be the most famous swimmer (because he was Tarzan). In the late 20th century, that title is reserved to Mark Spitz (because of his mustache and '70s Hair). In the early 21st century, it will be Michael Phelps or Ryan Lochte, but most especially the former due to his insanely high Olympic medal count (the highest ever in history at 18 gold, 2 silver, and 2 bronze).
Divers? Greg Lougainis and no one else. Tom Daley might pop up more recently.
Motor car racing will be an excuse to namedrop Juan Manuel Fangio (in the 1950s) or Michael Schumacher (in the 1990s).
Ask someone to mention a golfer and you'll get either 1) Tiger Woods (because he has dark skin), 2) Jack Nicklaus (unless people confuse him with Jack Nicholson), 3) Arnold Palmer (probably the oldest golfer anyone can remember), 4) Lee Trevino (because he was in some commercials for salsa dip), or Happy Gilmore (who isn't even real). Somebody might mention Fuzzy Zoeller just because he had a funny name.
If someone didn't know anything about basketball, they'd assume it's a one-on-one sport with all matches being between Michael Jordan and Shaquille O'Neil. Kareem Abdul-Jabbar might be referenced as well, due to his acting roles in films like "Airplane". Yao Ming has been popping up recently, and on very old works references may be made to Pistol Pete. If any other basketball player appears, expect it to be a contemporary with a licensing contract.
Anyone who has never taken a martial arts class always assumes that if it's done by Asian people, it's karate. Occasionally, they may call what they're seeing taek-won-do or kung-fu, the two other widely taught martial arts (even though there are many, many kinds of kung fu).
Many people don't even realize that Tai Chi is a martial art and not just a hippy exercise routine (hippies included!).
The popularity of Mixed Martial Arts has exposed more people to Jiu Jitsu and Muay Thai, but not much beyond that.
All martial arts are Chinese or Japanese. Except capoeira.
Krav maga has been getting mentioned more often. The fact that it's an Israeli martial art? Not so much. Only little. Prior to the 1960s, the only East Asian martial art most Westerners had ever heard of was judo (since judo was the only martial art practiced by Westerners at the time).
Before mixed martial arts came along in the 2000s, the list of famous martial artists was a pretty short one: Bruce Lee, Jackie Chan, Chow Yun-Fat, Steven Seagal, Jet Li, Chuck Norris, and a few others. Very few people know who Cynthia Rothrock is, even though the character of Sonya Blade in Mortal Kombat was directly based on her. Or Benny "The Jet" Urquidez, even though he helped to popularize karate in the West and is still the go-to guy in Hollywood when it comes to coordinating martial arts sequences in movies.