Thanks to the success of Toy Story, Finding Nemo and other works of Pixar, the movie biz is flooded with CGI children's movies. Nowadays, any animated movie must be computer-generated if is to have any chance against the viewing public, or face utter commercial failure. Hence the saying, traditional 2D animation is dead? or at least not meant to be taken seriously.
That's arguably, in large part, due to certain box office bombs of the past that have been animated in 2D such as Rock A Doodle and Happily Ever After. While most of these bombs were made by companies outside of Disney, Disney itself was not sparred. After The Emperor's New Groove, Disney movies would only experience huge success if they were CGI , which, conversely, helped fuel Pixar. One medium's failure is another medium's opportunity.
Disney gave 2D another chance with The Princess and the Frog. While successful, it was not as big a hit as they had hoped, thus resulting in them changing the animation on Tangled from 2D to 3D.
Disney do still try to make one 2D film for every 3D one they produce. After Tangled came Winnie The Pooh (though that was buried running alongside the juggernaut that is Harry Potter), and after Wreck-It Ralph will come Frozen. though this has been Tangled and will be produced in 3D CGI.
One exception is the popularity of The Simpsons Movie. But to be fair, The Simpsons has been around since 1989, and was obviously bound to do well, thanks to its already long-established worldwide appeal.
Ironically, Pixar is now developing traditional 2D films. The pendulum might yet swing back...
The success of Enchanted seems to have helped people realize that a genre/medium is not old technology, it isn't replaced just because something new and flashy comes along. Traditional animation will be coming back when people get tired of CG Animation.
Dreamworks must be the only animated film studio capable of copying off of its own movies. The commercial success of Madagascar begat their other animal movie, Over the Hedge. With that success, Disney finally gave Dreamworks a taste of their own unoriginal medicine with The Wild... Except The Wild was released after, but was in production before Madagascar, so they still ripped Disney off.
As The Nostalgia Chick and many others have pointed out, after Don Bluth had an awesome decade of the 1980s while Disney slumped, it turned the other way in the 1990s. Bluth gave in and tried to copy them. Anastasia is probably the most blatant try, even though it's a good movie in its own right.
X-Men was in production at the same time as Batman, both shows premiered within a month of each other, so it's not so much that one was truly following the other. If anything, its both shows who helped spawn their clones. Like the DCAU shows, Spider Man The Animated Series follows X-Men and included a lot of the people who had worked on the earlier show, like Avi Arad.
Disney's Gargoyles has been said could have be influenced by Batman:TAS, with its similar Timm Style art design, dark and moody atmosphere, and complex storylines.
The success of Scooby-Doo launched a whole boatload of other series about mystery-solving/crime-fighting teens and their talking animal/car/whatever friend. Most of these copycats were actually produced by Hanna-Barbera, the same studio that created Scooby-Doo.
There are so many clones that Boomerang has a block called "Those meddling kids" dedicated to Scooby Doo, and its many, many clones.
And even before that, the clones and the original had their own team on Laff A Lympics, the Scooby-Doobies.
Even the Licensed Games inspired imitators in the form of Battletoads and Cheetahmen. Both tried to spin off cartoon series as well, but the Battletoads cartoon flopped instantly and the Cheetahmen cartoon never got off the drawing boards.
Whilst the extent to which more adult-orientated animated shows such as Family Guy and South Park are direct 'rip-offs' of The Simpsons is a subject of bitter and acrimonious debate across the Internet, it is fairly safe to say that without the enduring popularity of The Simpsons, which showed there was a market for animated programming aimed at more adult audiences, the former two shows — plus a lot of more obscure and more quickly forgotten similar shows — would probably have never been greenlit thanks to the Animation Age Ghetto.
After the show first premiered, there were a number of prime time animated shows that came out afterward, like Capitol Critters and Fish Police, that lasted barely one season.
After the success of The Incredibles, more and more CGI-animated movies started mirroring its method of animating human characters with caricature proportions so as to create smoother human animation and avoid freaking out the audience.
Teen Titans set the tone for the past few years of kids' action cartoons. Comedy-action blending and Rule Of Cool became far more prominent, as did Animesque artwork (which was already gaining in popularity anyway).
This in turn caused Ben 10, whose success caused Cartoon Network to bring in more action cartoons to the network.
It could be argued that even Spongebob Squarepants took more than its share of inspiration from Ren and Stimpy, minus the gross-out humor (at first, at least). The two shows share loose artwork, manic pacing, surreal humor, hand-painted close-ups of the characters, and the same music cues.
Parodied in The Simpsons episode "Flaming Moe's". The episode revolves around bartender Moe stealing Homer's idea for a drink recipe and renaming it the Flaming Moe. He even goes as far to rename his bar after the drink. His bar becomes a popular club spot, attracting even the likes of Aerosmith. After Homer outs the recipe to the general public, dozens of bars, restaurants and carts sprout up on the same street with variations on the name- e.g., Flaming Meaux.
During the mid-1990s, Cartoon Network produced a coupleof cartoon series where the characters had very stylized designs, intentionally looked rather one-dimensional and were drawn with thick black outlines around their bodies (the style was intended to be a throwback to certain 1950s cartoons). After the success of The Powerpuff Girls in 1998, this style became enormously widely used in cartoons both by Cartoon Network and by other companies, and remain so to this day, partly thanks to the rise of Flash animation.
This ironically mirrors how Limited Animation caught on in the 1950's. It started out as a unique artistic statement, but later became an excuse to create cheap, lazy animation.