1. Andy Bernard
Andy was a breath of fresh air on The Office - a hopelessly awkward, stupidly ambitious sales rep with massive anger issues, endless nostalgia for his college years, and a penchant for a capella. He was a more believable office asshole than Dwight, and his behavior hinted at bizarre layers and vulnerabilities that The Office was great at exploring. Everything looked great for Andy Bernard to be a foil for the characters - and gave someone even Dwight could make fun of.
And then The Hangover happened - Ed Helms became a massive star, and they softened Andy's edges considerably. A bit slowly at first, but by the time Steve Carrell was exiting the show, they had turned Andy into a poor man's Michael Scott - a mostly well-meaning idiot with severe self-esteem issues, which only highlighted how worthless a once great character had become.
2. Homer Simpson
Homer is a near perfect comedic character - he's dumb (but not TOO dumb), he's mean (but not TOO mean), and - most of all - he cares a lot about his loved ones. Sure, he's deeply flawed and lazy, but he inevitably will come through for the ones he cares about, so we can care about him.
But like all things that go on too long (and good lord, does The Simpsons fit that bill), it gets ruined. With most comedies, characters will be pushed further and further into new extremes to exaggerate their funniest characteristics to the point where you can't find them believable and the things that made them funny have been pushed too far. This kind of thing has a term named after a Simpsons character even ("Flanderized"), but nothing represents this as well as Homer, who simply got too dumb, too mean, and too cartoonish (weird thing to say about an actual cartoon...) for any of his antics to have any comedic value left.
3. Chandler Bing
Chandler suffered the problem a lot of sitcom characters face at some point - he found happiness, which is basically the ultimate death knell for any comedy OR drama. Happy couples aren't interesting (see: Jim and Pam), because the key to any show is conflict. Happiness runs in direct opposition to conflict, so Chandler going from an awkward single guy who used sarcasm as a deflection for his own insecurities to a happily married, still kinda awkward guy mostly ruined what we loved about him: he was sorta miserable all the time. Could a loving relationship BE any more terrible?
4. Barney (The Simpsons)
The Simpsons was pretty great at fleshing out its massive supporting cast - episodes surrounding Apu, Krusty, and even Ralph delved into what made them tick and gave us a greater appreciation of them beyond their semi-one joke archetypes. However, this wasn't ever really possible with Barney - he was meant to be a one joke character for the most part: a disgusting barfly drunk who belched a lot. There were tiny attempts at fleshing him out - notably his film submission in the Critic crossover episode - but to really delve into Barney Gumble, it would need to address his rampant alcoholism - a pretty dark subject for The Simpsons to tackle. But they did - and the result they found was that once they had to examine Barney's insanely destructive lifestyle, they had to change it, making Barney sober. And sober Barney was a jokeless Barney - once you stripped away his one joke, there wasn't anything funny left. It was just sorta sad to see him around, not drinking and having a normal haircut. Barney always served as a reminder that Homer - while an alcoholic himself - wasn't the most hopeless drunk on the show. But with Barney sober, Homer suddenly became a little more of a loser, and the whole show got a little less funny and a lot more depressing.
5. Barney (How I Met Your Mother)
Barney was a popular character - probably the biggest breakout on How I Met Your Mother. And it's not hard to see why - Neil Patrick Harris kills it in the role, and he's a hilarious/ridiculous cartoon amongst a lot of very human mopery between Ted, Lily, Robin, and Marshall. The problem with having a super-popular character like Barney burst out is that there's a temptation to make them the center of the show (aka "The Urkel Factor"), and that's what happened with HIMYM (which was also something of a relief, since the actual main character - Ted - is one of the lamest TV protagonists in recent memory). However, in making near-rapist/definite sociopath Barney more central, they had to remove basically any characteristic of his that made him an entertaining character - which was all of the cartoonish qualities that made him look like a sexual predator piece of shit once you put him in actual storylines with other human beings and emotional connections.
It'd be like trying to give Kramer an emotional love story on Seinfeld - sure, you like Kramer, but it just feels WEIRD for him to have sincere emotions after being a broad cartoon for so many years.
6. Daenerys Stormborn
To be fair, the blame for this one lies at the feet of one George RR Martin. Daenerys is a tough character, primarily because she is SO separated from the entire rest of the Game of Thrones world, but also because we know where her character arc is ultimately going to go and the delay in getting there is BORING AS HELL. Daenerys is going to go to Westeros eventually, riding on her dragons. We know that's going to happen. It's going to be badass. The problem? It's been 5 fucking years and she isn't even close to doing it.
It's even worse in the books - which have been ongoing for 20 years - and she's in the same position, e.g. no immediate plans to ride her dragons into King's Landing. The wait wouldn't be so bad if there were compelling things happening in her plotline, but for the most part it's felt like the writers twiddling their thumbs - lots of hanging around a boring city yelling about how her dragons are missing, lots of dealing with the bureaucracy involved with ruling a small city, and lots of just sitting around not doing the one thing we wanna see her do - BEING BADASS WITH HER DRAGONS.
The last really cool thing Daenerys did was in season 3 - betraying the slavers who gave her the army of Unsullied by ordering her dragons to burn them all, and her new slave soldiers to turn on their former masters. Her calmness and certainty over the situation was that of the badass we knew would be strollin' into Westeros before long, and doing the same thing to the Lannisters or Freys or whoever got in her way.
Instead, she's been sitting on a throne, not hanging out with her dragons much, and generally not doing anything of interest. If we don't see Khaleesi riding a dragon straight into Ramsay Bolton's face within the next 6 months, I'm going to be super disappointed.