Lumpy Space Princess usually hangs out in episodes or scenes that call for a larger cast. She rarely contributes much when she does. However this is likely done on purpose, given her whole routine is to be like a spoiled teenager.
Jake was this in one episode when a witch stripped him of his magical fur that gave him his shape-shifting abilities, hampering Finn's mission to help regain his powers. It wasn't until Finn was in mortal danger that he finally snapped out of it.
Sokka from Avatar: The Last Airbender feels this way, at least sometimes, because he's basically the only one in the team who can't bend any element. Also, Toph remarks it when they are being chased by Azula and her tank. But while in some situations, Sokka's lack of bending makes him less threatening, he's often had great success with his boomerang, and it's basically his intellect that drives the other characters from Point A to B for pretty much the entire series' run. And he only gets better after he gets his sword (see Took a Level in Badass).
It is actually Iron Man who is somewhat the load of the team. This is highlighted when Captain America confronts Tony about his combat tactics which usually involve blasting a target or simply tackling it, making Tony very predictable and ineffective despite all the power his armor should be capable of. Steve even offers to train Tony in hand-to-hand combat, which if Tony had agreed to, would've probably made him the most effective team member.
Subverted in the case of Sue Storm when there was a breakout from the Skrull's ship and Madam Viper advises Captain America to leave Sue behind, since they would only be dead weight in their power-drained state. Captain America refuses and Sue would later protect the latter from an attack.
Ben 10: Alien Force: Alien X is a reality-bending Super Mode alien, the most powerful being in the universe. The problem is that Ben has to get a majority agreement on the tasks at hand with two other personalities within the alien. But seeing as they can't agree on anything, and are only slighly more likely to agree with Ben, the form is literally dead weight.
Aelita might count in the first two seasons, where her only form of defense, "Creativity", costs half of her life points, and she will die if she runs out of Life Points. She's only useful to stop XANA from attacking by deactivating towers he is using. In the 3rd season, she no longer dies when she loses all her Life Points, and she has an attack that is actually more powerful than those of the rest of the group.
In the real world, Sissi can either become The Load if she gets involved in the action, or surprisingly helpful. She's unpredictable like that.
Played with a lot in Futurama. Examples: The second episode, where they get stuck in a crater's quicksand on the Moon. Fry says "It's no use! Every man for himself!" Jumps out of the cart, gets stuck, then cries "Help me, Leela!" Or when Fry's head gets grafted onto Amy's shoulder.
Cubert in his first episode. They even disguise him as a hump on Fry's back at one point to sneak into a place.
Korporal Kretinus/Fugg in Insektors. How he manages to keep his job when he happens to be fairly thick is anyone's guess.
Inspector Gadget toys with this. The overwhelming majority of the time, the brainless detective is clueless to Claw's plan, spending most of his time bumbling or accusing the wrong guy while Penny and Brain do all the work for him. A fair few occasions however, his well-timed clumsiness actually helps them along the way.
There has also been a few episodes where he has actually learned that Penny was in trouble, and abruptly turned from The Load into an unstoppable forceto be reckoned with. This led to the popular fan theory that Gadget was once extremely competent yet suffers extreme PTSD from becoming a cyborg, and seeing Penny in danger reverts him to his former self.
Iron Man: Armored Adventures has Pepper Potts. She gets captured and rescued by Tony with surprising regularity, except for those occasions where Gene rescues her. She has an incredible knack for making bad situations worse and does very little to help Tony out, though to her credit she does try. Her efforts usually result in Tony yelling at her. However she is fully aware that she is The Load, which is why she wants a Power Armor of her own so she can be a more proactive member of the team. So when she finally does get her power armor, she shows full well she is no longer The Load.
Alexandra from Josie and the Pussycats. She mainly exists to cause trouble for everyone else. She isn't a band member and doesn't seem to have a job or an actual reason to hang out with them. (And no, chasing Alan the roadie doesn't count.)
Mostly averted with the sidekick Ron Stoppable in Kim Possible. Despite the fact that he sometimes does screw up the missions or needs to be saved, history has shown that he does save the mission more times than he screws them up, has Rufus in his pocket who saves the team every time the writers are too lazy to figure out a more clever way, and the first movie showed that Kim was practically a loser without Ron as her sidekick. Aside from the few times late in the series when Ron's intermittent monkey-theme superpowers kick in, his contributions are less than obvious, because they're almost entirely passive, but are actually quite important. Most notably, he does two things: transport Rufus (who's nearly as useful as Kim) to where he's needed, and keeps Kim inspired by his presence, and motivated by his being usually in some danger. The latter is usually only very weakly implied, but the aforementioned movie, and similar scenes in a couple serial episodes, made it very explicitly clear: in Ron's significant absence, Kim's effectiveness drops by a wide margin. The villain of the first movie arranged for them to be separated for precisely this reason. Another aspect of it is that his apparent incompetence makes him completely unpredictable, so no matter how good the villain's plan is, Ron can ruin it just because it could never have foreseen him.
Almost all of Hank Hill's friends and family are Loads on one level or another (and sometimes he himself is a Load to them!), but his wife Peggy really takes the cake with her raging ego and uselessness.
An interesting meta example in "The Return of Harmony". Discord attempts to drive her to cruelty by pointing out to her that she is The Load to her team. To his great surprise she proceeds to agree with every one of his insults in her usual kind, calm way much to the hilarity of the fans who know how badass she actually is, which forces Discord to straight up brainwash her instead. Basically, by agreeing she is The Load, Fluttershy almost makes a hole in Discord's evil plans and proves that she's not The Load at all—all without realizing it.
Interestingly, though, although there's no denying Fluttershy is a Badass Adorable, she does have a tendency to make things significantly worse, but then often fixes things later. An example of this would be the aforementioned "Dragonshy", but it also shows up in other episodes like "Swarm of the Century" with the parasprites and "The Sonic Rainboom" (although Rainbow Dash fixes that situation herself). There's also "Hurricane Fluttershy" when her timidness almost puts her in The Load category, but she ends up subverting it at the end of the episode.
Spike plays the role more straight, being a baby dragon, he has yet to gain much physical prowess and so is often useless or requires protection once a physical threat appears. In the role of Twilight's assistant however, he is thoroughly competent, so proves himself rather useful in emotional or intellectual manners at least.
Spike's physical weakness was actually the focus of Deconstruction in "Power Ponies", when he and the others are teleported into a comic book world, all the ponies gain impressive superhero personas while Spike...becomes the Plucky Comic Relief. Despite being perfectly convinced he will be no help, his Genre Savvy wits manage to help the other ponies (who are completely incompetent using their new powers at first) and later saving them from the supervillain using elaborate wits alone.
In the earlier episodes of Scooby-Doo included Scooby-Dumb (yes, that is his name), Scooby's inbred, hillbilly cousin. He is literally too dumb to be scared, and had to be dragged away from the various monsters. It takes something to make Scooby look smart and Scrappy look useful.
The Simpsons: Milhouse was this to Bart & Lisa when the Springfield elementary kids were stranded on an island. He forces them to carry him on a log over a chasm then he throws away the log before Bart & Lisa can cross because the kids chasing them are getting too close.
Antoine from Sonic Sat AM. He is incredibly cowardly and almost never contributes anything of value, yet for some reason they frequently bring him along on action missions.
Mysterio temporarily becomes a villainous example in the Villain Team-Up in Spider-Man the Animated Series. He has no powers to contribute to anything, only crates of stuff their quarry can knock down to block the villains' way when they are chasing a de-powered Spider-Man.
All the Channel 6 News Crew have become the Load at some point in the 1987 Teenage Mutant Ninja Turtles cartoon, but Vernon Fenwick is usually the biggest Load. He seems to exist just to make April O'Neil look like the more capable reporter, judging by the number of times he's fainted, run away, whined about getting a hard reporting assignment, or gotten captured by the Monster of the Week. It's no surprise that the Turtles can't stand him.
Total Drama Revenge of the Island has Cameron take his place in "The Enchanted Franken-Forest", complete with lampshade hanging from Zoey, who is forced to save him from mutant plants and pitfalls at every turn.
Zoey: (confessional) Is it just me, or am I doing everything while Cameron acts as mutant bait?
Cheetor in Beast Wars, but on an intermittent basis. Cheetor's relatively small size/firepower, impetuousness, immaturity, and lack of specialized skills can even verge on The Millstone. On the other hand, his speed and enthusiasm commonly enable him to fill a solid supporting role. Equally, he starts out as the load (and the resident trouble magnet), but throughout the series get powered up and matures into the Cheetor we see in Beast Machines. He's still fast, he's still impetuous but hell, he's scary good at what he does.
Almost the exact same thing could be said of Animated Bumblebee, for all his charm and humor. While he is okay at fighting human supervillains he is utterly useless when fighting Decepticons on his own, as his one weapon (nodes that shoot out beams of electricity) are too weak to even make any of them flinch. Well, until he gets the limiters on them taken off and they become the most powerful weapon on the entire team.
Averted with Sari who is somewhat of a liaison between humans and the Autobots as well as having a key empowered by the Allspark.
In Beast Machines, Rattrap takes over this position at the beginning because he has trouble transforming and, even when he does, doesn't have any actual weapons in robot form. The other characters, who previously viewed Rattrap as mildly annoying but a good guy to have on your side, start treating him increasingly as The Load. When Optimus is temporarily put out of commission and can't head off the other characters, they get downright hostile. Then they're surprised when Rattrap takes drastic measures to get some firepower.
In Transformers Prime, Miko has this bad, possessing all the survival instincts of a lemming with nothing left to live for. Not even months of experience is enough to teach her that, no, she can't be of much help on the battlefield, and no, it is not safe for a squishy human to be around giant robot fights. Surprisingly, the other two Team Pet human kids are actually helpful, one in an information-providing capacity, and the other having actually slowed down or temporarily defeated Decepticons once or twice. Though she's getting better in recent episodes.