Two Gamers On A Couch is an archetype of the Webcomics medium. Many of the most popular webcomics (and the people who read and write them) have an interest in Video Games, and the two gamers on the couch, playing games and shooting the breeze about whatever crosses their minds, is the purest expression of this fanbase/author background.
Two male friends, frequently Author Avatars of the artist and writer of the series, play computer games and have hijinks, mixing in political ideas and unexplained or explainable phenomena that surround their lives. Hilarity Ensues.
The two roommates/friends will often borrow from the archetype of the Straight Man and Wise Guy: One will be wacky and insane, whose passion for computer games and other aspects of nerd culture will result in stupid, crazy, illegal and (hopefully) amusing repercussions. The second will be more down to earth, calm and intelligent — not above being pulled into the wacky one's schemes, but usually knowing when to pull out. He usually has a stable, "normal" career whereas the wacky one will either be unemployed or painfully incompetent at whatever they do.
Sometimes this is expanded into a Comic Trio, when they are accompanied by one or more characters who provide context, perspective, or episode-specific references. These may range from a Talking Animal or a Dungeonmaster's Girlfriend to a Gamer Chick, Nerd Nanny, Robot Buddy, Monster Roommate, a Time Traveller, a character from the franchise being reviewed or any other unexplained supernatural or Sci-Fi element that serves as a plot device and may or may not change on a per-episode basis. Most of these series are set in the "real world" and these fantastical elements are handwaved as really cool.
Love interests as stand-ins for the authors' actual wives or girlfriends (assuming that the author has spoken to a girl in his life) are common as are actual Author Avatars who appear in one-off strips and comment on production or philosophical nonsense.
Penny Arcade: The flagship Two Gamers On A Couch series. Gabe and Tycho (who switch between crazy and sane depending on the plot) are the gamers. This series is the most politically active, making massive amounts of cash from their comic and related projects; they run a gaming expo and a children's charity on the back of the comic. They publish Spin-Off comics of their comics, have also produced their own computer game, and have been featured as an expansion of a moderately successful collectible card game.
The first strips actually poked fun at this very trope, and tried really hard not to use it very much.
Garnet And Gure features Garnet, a buffoonish latter-day gamer and Gure, a painfully emotionless old-schooler.
Brawl in the Family: King Dedede discusses the flaws of Super Smash Bros Brawl to Kirby, who's happily playing the game on the couch. Lampshaded Fridge Logic, how King Dedede is complaining about the game where he made his first SSB debut. 
Comic 357 "Bowling" features Kirby, Diddy Kong, and Adeleine playing Wii Bowling on a couch.
PVP: A clear inversion. Despite it also centering around gaming, none of the main characters are gamers on a couch.
It USED to be a pretty good example of this trope. There were two guys named Robbie and Jase who spent a lot of time on the couch facing the viewer playing video games. But the focus slowly shifted away from those character, and from gaming in general. Eventually Robbie won the lottery, moved into a huge mansion, and had a falling-out with Jase.
Rob and Elliot: Elliot is the sane/normal school teacher, Rob is the wacky and over-the-top drama queen. Of course, Elliot is only sane in relation to Rob; one arc revolved around his being Not so Above It All when trying to find a new roommate. Doctor Doom(sday) is their megalomaniac next door neighbour, who frequently gets in trouble with the Justice League.
More like two guys sharing an apartment, as gaming doesn't actually factor into it, but otherwise it fits the trope.
Applegeeks: Started off as a TGOAC comic but quickly evolved into a more dramatic model. The wacky hawk (Mad ScientistSuperhero) was the crazy one and he had many friends who took on the sane side of the dynamic. After the creation of Eve, the Mac-based andoid, the series changed dramatically into a serious action/drama series, and recently became wacky again.
A slightly alternate interpretation involves copious amounts of Unreliable Narrator. The squirrel does talk to him, after all.
VG Cats: The avatars of two cats who "act the part" of characters in different computer and console games — we never actually see the couch, just the two characters inside the game, but it fits the same format.
The cats are occasionally seen in the real world, when parodying tabletop games or buying a new videogame.
Real Life Comics: Gaming is part of the overall geekery of the author's interests. Cast of Characters has fluctuated on the author's real life associations. Usually the Author Avatar is wacky, while his wife is sane — but for some situations, it's reversed.
To elaborate, panels with text added to them are divided into first panels, second panels, and third panels. Each time you look at the page, a first panel, a second panel, and a third panel are randomly chosen. And hopefully, the combination is funny. Hopefully.
Sluggy Freelance was arguably this for its first week of strips, with Torg checking in each day on Riff's computer problems, such as summoning the Devil and the archangel Chuck onto his hard drive, who proceed to get into a Quake death match. The series quickly expanded far beyond this, however. Video games and random conversation between the Heterosexual Life-Partners do still appear in the strip, but are only one aspect of the increasingly bizarre and complex storylines.
Sweet Bro and Hella Jeff is ostensibly this, as it started life as a direct parody of a generic Two Gamers On A Couch comic posted on the Penny Arcade forums. In practice, while the theme is still definitely there (as far as anyone can tell), it's not quite as focused on gaming - only a small number of episodes make reference to playing games, and the only time Bro and Jeff are actually seen on a couch playing games quickly descends into... something else.
Shaun of the Dead starts off two one of the two guys (Shaun) questioning his half of the couch, and throughout the movie, tries to reorganize his life and his relationships... but in the film's final scene, he's back where he's happiest, sitting on the couch playing video games with Ed, who's now a zombie but still able to play TimeSplitters.
Gorillaz short "Game of Death" has 2D and Murdoc playing a fighting game, with Noodle and Russell as their respective characters.
Other Web-based Media
Spoofed in Homestar Runner, in which Strong Bad quips that most webcomics are about "slickly drawn college roommates [who] make nothing but video game inside jokes"; cut to a Penny Arcade-like comic of Strong Bad and Strong Sad doing just that.
CouchCouple, a YouTube channel that consists of mostly of Let's Play's and tutorials, pretty much runs on this. Ben being the crazier one of the two, and always searching for secrets, and Jo being a bit calmer, who prefers to do the main quest.
‘‘Videogames Awesome'' has been Five Friends On A Couch for a great deal of its run, until other commitments got in the way of getting everyone together on a regular basis."Four Player Friday" still happen frequently, even if it's with more than four people. (Or not on a friday.)
Yahtzee Croshaw and Gabriel Morton are essentially Two Gamers In Yahtzee's Apartment when they record the Let's Drown Out series of videos—hour-long stream of consciousness recordings of one of the two playing a dull-to-watch or poorly constructed game (or the occasional good game) of times past whilst either critiquing the game, talking about gaming news, or being Vitriolic Best Buds.