The animation of Happy Tree Friends became more polished over time, while episode plots became longer and more likely to involve multiple characters. This is particularly notable in the TV episodes starting in 2006.
Homestar Runner's first major cartoons (which have since been removed from its site) were fairly awkward and at odds in characterisation with later installments. Around the point of the Fluffy Puff Commercial or Where's The Cheat, the characters started to reach their current form.
The Strong Bad Emails have almost always been the main draw for the site, and grew its beard when the show became longer and had more outdoors scenes. A decent bet would be the first Compy email "invisibility", which is a prime example of Strong Bad's Imagine Spots
I'm a Marvel... And I'm a DC began as some somewhat amusing shorts, though it relied a bit on sticking to the Mac ad series, and the stop motion was rather jarring. The series really got funny when it just picked up the concept of a dick-waving contest between the two giants and ran with it. In other words, the second RandomGuy's Green Goblin showed up.
Also on the dramatic side, it grew a dramatic beard the moment it revealed that Superman was missing, and the casual "After Hours" had suddenly become a Crisis Crossover.
Related to this was Lex Luthor and Superman's argument about erasing the Marvel universe when viewers suddenly realized the series could also be incredibly deep.
It grew the beard a second time, going from great to awesome, by adding one character - Deadpool. "Rorschach and Deadpoooooool. A nut and a fooooooooool."
Neurotically Yours had very rough animation and was mostly about a squirrel rambling on about what bothered him in the world and a teenage goth girl who kept the squirrel as a pet while listening to punk music and was extremely introverted. Several episodes later, the series quickly evolved with the squirrel, Foamy, giving more coherent and thoughtful rants while also causing shenanigans. The girl, Germaine, also had her own rants and slowly shed her goth persona of the course of several years, revealing a broken and battered girl.
Red vs. Blue first started off as a novel concept, but all but two of the actors were amateur, the sound was muffled and the overall pacing was slow. Season two picked things up immensely, but season three was really where Rooster Teeth got into the swing of things.
The real growing the beard moment came with the Recollections trilogy. Blood Gulch Chronicles was undoubtedly hilarious but there were arguably just as many shows out there that were just as good if not better. Then came the Recollections trilogy with EPIC!! fight scenes interesting plot/character development, surprisingly good acting, an awesome villain and a really gripping story, and it STILL managed to stay absolutely hilarious. All this served to finally cement Red vs Blue up there as the greatest Web show of all time, with quality on the level of the best of professionally made movies
Now, with Season 10, Elijah Wood signed on as one of the voice actors.
Episode 8 of RWBY is considered the point where the series picked up and really came into its own, featuring Character Development, setting up for the rest of the series and the action sequences that had been expected from the start.
The first two episodes of There she is!! are great, but it isn't until the third episode that the story really starts to pick up. This is mostly because, while the first two are pretty much standalone stories, the last three episodes work as a trilogy.