Achewood began life as a hit-and-miss gag strip about a house full of "alive stuffed animals," but with The Party arc it began to develop into a complex, layered, plot-and-character-driven slacker epic.
Though it took off quickly, the first few storylines of The Adventures of Dr. McNinja were rather different than the current blend of awesome and funny it is today. Chris Hastings himself advises new readers not to start with the first, Ronald McDonald-centric story. The next two stories, while well-done and humorous, were essentially setting up the character and playing off a tired "pirates vs. ninjas" theme. The comic really hit its Cool Versus Awesome-plus-funny stride in the 4th story arc. Specifically on this page.
A Loonatic's Tale began in 2007 as a comic the artist/co-writer drew in her spare time at school, with poor art and writing and awkward layouts that culminated in a style switch (including dropping colour from the pages) halfway through the third storyline. Then the comic went on a several-month hiatus during which the artist entered a few Original Character Tournaments, started attending art college and generally worked on improving her craft. Now the comic is back in full colour, and both writing and art have greatly improved in quality.
Black Adventures really got its act together in the third chapter when the story became more tied in with the games and the writing got more consistent.
The beginning of Bob and George is all but a mess. Random filler strips, jokes that don't quite take off, and the occasional hint that, at some point, there would be a drawn webcomic with Bob and George. Once the last part was completely eliminated and the "Just Another Day" arc started, it finally got into its true plot and humor.
Boxer Hockey started off with sub-par to decent art, had a cast of generally cliche charactersnote A dumb character, who shared a nickname with the author, the jerk, The Big Guy, the Only Sane Man, and their coach., and sometimes relied on Black Comedy and gay jokes. During the strip's four-year life, Tyson Hesse, the author, attended college. Over the years, it resulted in the cast having heavy development, well thought-out jokes, and absolutely beautiful art. Tyson Hesse is now considered a professional artist, and is doing freelance jobs for Reverge Labs and Dark Horse Comics. In short, it went from this, to this, then finally to this, and improves every day.
The beginning of Dan and Mab's Furry Adventures , to be frank, absolutely sucked. Then the author resumed updating after a year's absence, at which point the art quality massively improved, the characters' personalities became more distinct, the plot picked up, the worldbuilding started to improve, the separate species were introduced... In general, it just, very abruptly, became worth reading.
Dead Of Summer grew its beard around the halfway point of Book 1, as they focused less on the Ludicrous Gibs and more on Character Development. The Art Evolution happened around that time too, resulting in more detailed, clearer drawings. The beard was fully grown by the time Book 2 rolled around; things soon became very character-driven. And then The Protomen show up.
The Dragon Doctors: The strip began as a one-shot for a group of TF fetishistsfans, and the apparent hasty writing of the first half of the first chapter reflects this. As the author begins fleshing out the world, the comic gets much more interesting.
El Goonish Shive started to grow the beard with the Sister arc and finished at the end of Grace's Birthday Party.
Go Get a Roomie! begins as a light hearted gag-strip with some cheap humor centering around a polyamorous protagonist. The series then gains a Deuteragonist as a direct personality counter and the series takes off from there.
Megatokyo starts off as a fairly standard 4-panel comic with two video game guys getting into hijinks. It takes about fifty strips before it gets into the ridiculous multi-person romance and off-the-wall zombie-robot-Godzilla adventures at the same time.
1/0 had no point save getting a girlfriend when it started, nor did Tailsteak have any art experience, and it shows. The reason there was No Fourth Wall was that Tailsteak never bothered to put one in, and found he couldn't do much in the way of jokes with one. Then he started taking real advantage of its absence, using it for creative character interactions. Then said characters started spiraling out of control in just the right ways.
The Order of the Stick grew a beard over the course of the second arc, which saw it move away from its origins as a series of gags about D&D rules and add character development and a more complex plot, as well as improved art. Improvements continued through the third story arc, and it's been fantastic ever since then.
The trope is also lampshaded: upon his reunion with Haley, Elan demonstrates unusual (for him) wisdom regarding outer appearances, and Haley mentions that she half-expected him to "grow a beard". And he has, figuratively speaking.
Our Little Adventure, about 80 or so pages in. The characters look less wonky and the story starts to seriously move.
The exact moment Penny Arcade started being funny can be narrowed down somewhat definitively to "Claw Shrimp." It's definitely the oldest strip you'll hear referenced.
While writing the first few comics of Princess Pi, Peter Paltridge seemed conflicted between his desire to give Princess Pi genuinely threatening villains, and his desire to make her adventures as random as possible. This resulted in comics that went too straightforward to allow randomness, and some where the randomness overpowered the conflict. He claimed to have eventually found a "groove" with "Princess Pi vs. The Alpha Bitch". Indeed, the story does an entertaining job of creating random threats without losing sight of the main conflict.
The definite beginning of the comic's "beard" is the end of Act 3, when "[S]: Enter" displays just how incredible the flash format could be.
The 500th strip of Questionable Content is universally recognized as a turning point, when the strip began focusing less on one-off gags and introduced some real character development and plot arcs. The art was also steadily improving throughout the series.
Some fans would state that Slightly Damned grew the beard when Rhea and Buwaro escape from the Ring of the Slightly Damned and meet Kieri. This is not only when the storyline really picks up, but when the improvement of the artwork starts becoming more noticable.
Twisted Kaiju Theater started as a small time comic strip with endless toliet humor. It ended up becoming one of the longest running web comics ever and dealing with many dark, mature themes while never losing it's comedic value.
Two Evil Scientists started as a fairly decent Sonic and Mega Man crossover comic, with the first few arcs showing the heroes of the Sonic and Mega Man series battling the titular scientist's robots. The story took a unique turn following the Metal Devil arc, and the quality's been going up since then with no sign of stopping.
When The Way of the Metagamer started, it was a shameless The Order of the Stick ripoff, with one-dimensional characters and lacking originality or humor. The creator realized this, and put in a scheduled Series Hiatus while he improved his skills. After the hiatus, the plot (yes, there was one in the beginning) picked up, the readers get some idea of what is going on, there is an epic showdown between Jane and Captain Obvious, and the series steadily became more Troperiffic, to the point where Tropetan herself appears and then the story goes Off the Rails. However, after the time-travel arc, one can argue that the series has shaved its beard off, as the story came to a screeching halt while the author showed just how much of a weeaboo he is.
xkcd started out as a merely okay collection of sketches and comics the author made when he was bored. Then, with comic #70 it finally grew into the intelligent gag strip we all know and love.
Zap! Starts out as a classic Space Opera Amnesic protagonist origin story and slowly becomes an epic tale of mind-control backstabbing and various alien factions.