Piggy is the best example. She used to be a full-blooded, vunerable character with some extreme narcissim and nerosis. One of the ways Frank Oz explained her essence as "a truck driver who wants to be a woman." Then, somewhere around 2000, she was slimmed down to a character who resolved everything with a karate chop. She became pure physical comedy, and not very good physical comedy, either.
Now, one can argue that she didn't have a chance to be herself, because the Muppets only had a few (pretty crummy) TV movies and a handful of apperances. In "The Muppets" she definately started to return to her old, complicated self. But if you look at the apperances when Oz was still handling her, she was still written better, and did more than just beat the frog up. Part of this may be due to the fact that Oz created the character, had her longer, and was very particular about what she said and did.
Exactly. Plus, she's almost always grumpy and acts more like an overprotective or abusive parent towards the frog with a somewhat dictator-like attitude. And Kermit is too afraid to put her in her place these days as well, whereas Jim's Kermit actually did have the guts to stand up to her and punish her when he had to (like in the Dom DeLuise and Loretta Swit episodes of TMS). Kermit wasn't even afraid to fire her or even threaten her with a firing. And he could easily do it again.
She has also seemed to regress back to her over-the-top aggressive side that was most prevelant in the first three seasons of TMS and with her relationship with Kermit seems to have reverted back to its original "Stalker with a Crush" form rather than continuing the more developed, complex version of their relationship that it was developed and domesticated into before TMS ended and throughout the 1980's.
Even things that have been written in in-character press releases and interview articles for her to say have gone against her personality and taken to extremes that even she never really went to (such as Piggy saying "As soon as Amy Adams learned the rules of not touching the frog", Kermit saying "Piggy wouldn't let me near Amy Adams", Kermit saying that he won't say who his other favorite female artists because Piggy won't let him, etc.). All of which is just plain STUPID and makes their relationship come off as an abusive one rather than the loving, complex one that we would much rather see. Good relationships are built on understandings, not abuse!
She also didn't always barge in when the frog had intimate moments with female celebrities/guest stars and seldom, if ever, got mad when he did duets with other women or got hugs or kisses from them ("Friends hug! Friends don't spy!"--a valuable lesson that the modern Piggy has clearly forgotten about and needs to re-learn). As the characters and their relationship evolved, the frog and pig did seem to have an understanding in regards to all that, even when the frog did appear with other women or when Piggy appeared with other men. I give you the fact that such understanding seemed to be non-existent in the first three seasons of TMS, but still, the fact remains that they had an understanding and remained loyal to each other and never cheated, no matter what.
Not only that. The pig did recieve her share of negative karma in the past as well, especially when she really crossed the line (like in the Dom DeLuise, Leslie Uggams, Lynn Redgrave and Loretta Swit TMS episodes). Today, she has not only lost her vulnerability, but she's now practically a "Karma Houdini" (to borrow another trope from TVTropes.org) and never gets her comeuppance when she really should (even though the ending of the Muppets' Good Luck Charlie guest episode should be edited out of all future broadcasts due to the pig getting way too out-of-character, something bad should've at least happened to Piggy, similar to her failed attempt at chopping Big Bird).
And when Piggy did use karate, it was only when she felt insulted or was actually provoked. Even then, when she did chop another character, it was usually because they actually deserved it (like with Kermit in the Lena Horne TMS episode, Fozzie in the Candice Bergen TMS episode, the various Muppet movie villains, etc.). Even then, there was usually some sort of build-up that occured before she resorted to a karate chop (like in the aforementioned TMS episodes).
Heck, there were even quite a few Muppet productions where Piggy didn't use karate at all or did not threaten anyone in any way (such as A Muppet Family Christmas). The writers, including Jim Lewis and Kirk Thatcher, should not feel obligated to put chops or threats into every Piggy appearance--it's gotten old and was better off being used sparingly.
So, to Lewis, Thatcher, Jacobson, et al., please take all of this to heart when writing for Piggy again in the future. Stop making her into the one-dimensional character that she has been Flanderized into and restore her original complexities! It would make her character a lot more likable again (hope TM is only the beginning of her character regaining her complexities and hope the other writers will continue that).