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.
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.
How well Peter Parker actually works as an Everyman is of course open to debate. He is not just highly intelligent, but in his very first appearances he was shown to be a scientific genius, able to come up with the web-formula and construct web-shooters and Spider-tracers while still in his teens and whip up a formula to turn the Lizard back into Curt Connors in a matter of hours. He is also the orphaned son of two super secret agents and always had several highly attractive women vying for his attention. And of course he only comes across as something approaching "average" when you compare him to the right people - i. e. Reed Richards, but not the Thing (who also has been described as an Everyman), the Invisible Woman or the Human Torch, to Iron Man and Thor, but not to Captain America (see below), Daredevil or Iceman.
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.
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.
Arguably Robinson Crusoe. An average Englishman from late 17th century stranded on inhabitated island. He got no particular set of skills nor character traits (at least for his epoche), yet is able to hold on his own for two decades. Not to mention his adventures before he got ship-wrecked.
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 Nineteen Eighty-Four, 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.
Ernie from Piranha Club started as something of a loser but through reverse Flanderization, he eventually become one.
Goat in Pearls Before Swine. He's the only character who reacts to (or even notices) the weirdness that surrounds them in the same way the audience would.
Charlie Brown. You can't help but identify with him. Charles Shultz relates a letter he got from a fan, who said "my son came home from school one day with a sad frown, slammed his bookbag to the floor, and said, 'Mom, I feel just like Charlie Brown.' He didn't have to say another word. I knew exactly how he felt."
The headless titular character in Quidam is literally an Everyman (the word 'Quidam' means 'nameless passerby', and the soundtrack album version of the title song has the male singer explicitly state "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.
The play Everyman is about an Everyman going on an adventure to Death.
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.
Visual novels, dating sims and eroges tend to have blank slate protagonists so the player can step into the role more easily.
In later seasons, if the authors were feeling particularly conservative that week, he started giving lengthy Author Filibusters 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.
Charlie Collins from the Batman: The Animated Series episode "The Joker's Favor" fits the description to a T, and that was the whole point. The fact that the Joker would spend two years keeping track of this poor guy only to find him and sadistically hold him up to a promise later, even though it didn't benefit him in the least, only serves to show what a monster he is.