A character who is mostly a blank slate stand in for the audience, made to be empathetic to all. They won't be exceptional; in fact, they will be decidedly average. If you try to pin down the character traits of any one of them, you'll probably come up blank. They are usually popular by association, in that they tend to interact and be friends with a large group of more interesting supporting characters.
The Everyman really has no distinct personality, except what is defined by others' interactions with them. They end up being the Designated Hero, despite them having no real abilities that qualify them for the job. On the other hand, they don't have any abilities that mean they shouldn't take the job, either. One gets the distinct feeling that if people weren't trying to kill them / wacky circumstances didn't happen to them / the fate of the world didn't fall into their laps / their wacky neighbors weren't around, The Everyman would be the most boring person in the world.
If a leader, then they're a Standardized Leader. The videogame version of this is a Heroic Mime in terms of plot, Jack of All Stats in terms of ability, and a Featureless Protagonist when taken to its extreme. May 'evolve' into an Extreme Doormat.
In Dom Coms, the father is often an everyman, struggling just to maintain sanity in his family and keep it together through the zany schemes set up by the wife or kids.
Not every character created with the intention of being The Everyman actually stays that way. If the writers think Viewers Are Morons, then this character can quickly devolve into a Loser Archetype, with the idea that this is how the average person acts. At this point, the character's message sort of devolves into telling viewers "This Loser Is You".
Despite the name, everymen aren't Always Male. But they usually are, because Most Writers Are Male.
Often an Audience Surrogate. If so, you may expect them to be:
A default character for the audience to latch on to, as a sufficient blank slate that the audience will know we are "expected" to identify with said character; and love will come later. This can be useful in an unfamiliar setting; compare The Watson. As the story develops, this type of Everyman may devolve into an inoffensive Foil or Supporting Protagonist. The audience may find them harmlessly uninteresting or worse, and latch onto the action hero, Ensemble Dark Horse, or villain instead.
An empty vessel for the audience's hopes, dreams and aspirations. (Not to be confused with an Escapist Character who already possesses what the audience craves.) These are the sort of Everyman characters where each audience member is willing to imagine themselves in the character's shoes, with no apparent contradiction. This may lead to some complication (or crowning moment) when the author forces them to undergo some courseof action that the audience, having already invested in the character, would not (at first) imagine themselves taking.
His (unintentional?) expy Kosuda in B Gata H Kei is an ordinary schoolboy trying to make sense of Yamada's WANT/DO NOT WANT/WANT/DO NOT WANT behaviour.
The Producer in the anime version of THE iDOLM@STER. Even his description is nondescript.
Peter Parker/Spider-Man is often held up as the epitome of this within superhero comics, and possibly the key to the franchise success. Admittedly, he's not a strict example, as he's consistently portrayed as responsible, hardworking, highly intelligent, and when the going gets tough, a wiseass. However, compare him to his contemporaries: he's the average working stiff where the others include super-scientists, a millionaire playboy, an idolized war hero, and a god. Some writers (Joe Quesada especially) tend to turn this into This Loser Is You, though. He fills the role so perfectly, many other attempts to make an Everyman superhero wind up compared to him.
The original Freedom Fighters seemed to have evolved this way in Sonic the Hedgehog, likely to act as foils to Sonic and the more abrasive additions from the games. A lot of their shortcomings are rather subdued or down more to circumstance than having prominant personality defects, and while a lot have unique abilities, they are played in a more realistic manner than their super powered comrades. This is less prominant in earlier issues and the coinciding TV show, where they have goofier, more prominant personality defects, but they still had visible shades of this at times.
Films — Live-Action
Wikus, the "protagonist" of District 9 is a deconstruction of this trope. Whether he's a Punch Clock Villain, Idiot Hero, or Jerkass Woobie is entirely up to interpretation. Ultimately, he reacts to extreme circumstances (that demand heroism) just as you'd expect an average nerdy professional bureaucrat thrust into a dangerous and unpredictable environment: poorly.
Joe, the main character of Idiocracy is described as the most average man in existence. The speaker then shows a series of graphs, all of which have Joe at the exact middle of the bell curve, a trend which he describes as "remarkable." It is unclear if he sees the irony.
Of Mice and Men has George, largely made distinctive by his relation to Lenny.
Dr. Watson fills this role in the Sherlock Holmes stories. He does have certain distinct personality traits, such as his eye for attractive women (how unusual), but in many other ways he reflects the typical Victorian citizen who read Arthur Conan Doyle's stories when they were first published, bridging the gap between the readers and the otherwise eccentric Holmes.
The title character of Alice in Wonderland is a fairly unremarkable Victorian child, in order to better contrast with the insanity of Wonderland
Winston Smith in 1984, whose sympathetic human characterization is said by O'Brien to be "the last man."
Mickey Smith and Rory Williams are both very deliberately ordinary people whose girlfriends become the Doctor's companions and end up crushing on him. A great deal is made of the contrast between the ordinary, happy life they could offer, and the adventurous, extraordinary one the Doctor provides. In Mickey's case, he is somewhat unceremoniously dumped in favour of the Doctor, with Rory, the episode "Amy's Choice" makes it clear that, despite her zigzagging feelings for both of them, if it came down to a choice between the two she'd choose an ordinary life with Rory.
The usual Cirque du Soleil protagonist (if the show has a protagonist) is a version of this: see Quidam, "O", La Nouba, Corteo, KOOZA, even the Delirium concert tour. Often they are pulled into the plot by a Trickster. In "O", it's set up that he appears to be an audience member.
The headless titular character in Quidam is literally an Everyman (the word 'Quidam' means 'nameless passerby', and the song 'Quidam' explicitly states "I'm everyman"), but the main character Zoe is also a, less literal, Everygirl. With an Everyfamily made up of an Everyman and an Everywoman. It... gets a little bit confusing.
Claude of Star Ocean The Second Story, who is even easier to identify with because the game's Private Action system allows you to choose many actions that show what kind of a person he is.
In Final Fantasy XII, Basch was originally intended to be the main character, but it was later switched to Idiot Hero Vaan because the creators thought that he would have more of an Everyman appeal.
Dave in Maniac Mansion. He's Sandy's boyfriend, but other than that, he's pretty much just an Everyman. And while the other six characters can play an instrument (Syd/Razor), fix radios and/or telephones (Bernard/Jeff, although Jeff can only fix telephones), develop rolls of film (Michael), and proofread manuscripts (Wendy), Dave has no abilities or talents at all. Sadly, since he's the also the lead character, he's also the only one you can't NOT choose.
Several of the survivor characters in the Left 4 Dead series fall into the everyman trope:
Louis works at the IT department of an electronics store and plays video games. Other than going to a gun rage on his lunch breaks, Louis doesn't do anything else out of the ordinary.
Zoey is a college student whose parents are separated. She's a huge fan of zombie films as well, but nothing else stands out about her.
Coach is a high school health teacher whose knees were injured from college football in his younger days.
Ellis is a mechanic who occasionally plays in a band with his buddies during his downtime.
In later seasons, if the authors were feeling particularly conservative that week, he started giving lengthy Author Fillibusters on the evils of McMansions, gratuitous lawsuits, gentrification, Hipsters, protesters, the porn industry, etc and ended up simply being right without any sort of comedic twist.
Nitz in Undergrads. He's lazy and sarcastic, but far less "out there" than any of his friends, and is known for having few extreme interests or opinions.
Rufus and Amberley in The Dreamstone for the line of work they had, were portrayed as rather normal acting kids who usually handle their jobs in a rather uneventful and conflictless manner until the Urpneys break the normality of things. Less prominant in earlier episodes where they are slightly wackier and brattier (something that actually cost Rufus at least three everyman jobs beforehand).
Tommy Pickles in Seasons 4 and later on in Rugrats.