The Amazing Race: There's at least one racer per season that's completely useless on tasks, dragging down their teammate.
Buck Rogers in the 25th Century: Doctor Goodfellow, the resident "scientist" aboard Searcher in the second season, whose occasional contributions as Mr. Exposition were vastly outweighed by his bumbling mannerisms, inability to control his curiosity, and an utter lack of basic self-preservation instincts. Searcher and its complement could have avoided at least half of their problems if he had been Thrown Out the Airlock and Buck, Wilma, or Hawk had asked for a scientist with a brain, instead of trying to protect someone so self-evidently Too Dumb to Live.
Wesley was this when he first appeared on Buffy. Aside from being a not-very-effective tyrant, he was inexperienced, his attempts to help the other protagonists usually just made things even worse, and the number of times he was actually useful could be counted on one hand. He got a lot better when he was moved to Angel, however.
In "The Zeppo," Xander worries that he is the Load, and the other characters agree and treat him that way. Buffy then excludes him from the group's activities against the threat of the week. He spends the rest of the episode saving the school, and the world, from a completely separate threat, while the rest of the characters deal with what they think is the main threat in the background. Of course, in most episodes Xander was actually very effective at contributing to the group, making his sudden "uselessness" in this episode pretty incongruous.
There's Chuck. At the start much of the show's humor came from demonstrating someone in so far over his head he's in danger of being crushed by the pressure. He also demonstrates erratic competence, often managing to both save the day and act as The Load in the same episode. He has largelyoutgrown this now, and is actually pretty darn competent much of the time.
Plenty of companions qualify for this trope, especiallythe female ones, with the most well-known examples being Tegan, Susan and Peri. The new series has thankfully avoided this, making the companions useful while still being outshone by the Doctor.
With the possible exception of Adam Mitchell, who borders on The Millstone, especially in The Long Game. Note, however, that for once the Doctor dumps him as soon as his status becomes clear. Also take note that Adam was only invited because of Rose's poor judgement of his character (plus it was strongly hinted that she invited him because he was in the Doctor's words, a "bit pretty"). The Doctor wasn't so sure, and the Doctor always chooses companions whom he knows without a doubt will rise to the occasion.
In the post 2005 series, The Doctor makes a point of refusing to allow anyone who are too small-minded or unimaginative or fearful of the unkown to join him on his adventures because he knows they would end up being The Load or The Millstone. In fact, he nearly left Rose in the wrong timeline because she came dangerously close to being The Millstone when she tried to alter the timeline by saving her doomed father in the episode "Father's Day".
The Doctor even pre-judged certain characters as The Load like Mickey and Amy's fiancé, Rory. Until Mickey spent the second half of season 2 in a parallel earth as a resistance fighter, and Rory spent two thousand years as an immortal auton guarding Amy in stasis inside the Pandorica. The Doctor is surprised and proud of them both for having proved him wrong.
Just being around the Doctor seems to have a de-Loadifying effect. Jackie Tyler was pretty much The Load in her early appearances, not so much in the later ones. Just don't let her try to help pilot the Tardis.
Farscape: Stark, who gets promoted to the main cast to replace Zhaan after she gets Killed Off for Real. Except that, unlike Zhaan, Stark has no particularly useful skills and is generally either borderline catatonic or engaging in psychotic fits that endanger the other characters.
Firefly: River Tam's "wanted" status generates conflict between the crewmembers by forcing them to avoid lucrative jobs that would involve too much oversight and poses a risk of arrest whenever they come into contact with government agents. That is, until she Took a Level in Badass for the movie. Of course, her brother and protector, Simon, acts as The Counterwieght by being a very useful doctor and occasional heist planner for the crew, of a talent the crew would not otherwise have access to, if not for the fact that he and River are on the run. Justified in that even without Simon, the crew (with the exception of Jayne) would never have the heart to dump a cripplingly insane girl with the Alliance, especially since they made her that way. It should also be noted that River's telepathy has saved the crew's ass more than once, both in the series and the movie. And, of course, she almost certainly would have continued to be progressively more helpful had the series gone on for more than one season.
The King of Queens: Arthur contributes nothing to the household and in fact has cost the Heffernans significant amounts of money (Started fires, sold their furniture when they are away...etc.) and stress (goes through personal belongings, keeps them awake at night when moved across the hall, constantly yelling and trying to force his rules on them...etc). Whenever he comes across some money like bingo winnings, he doesn't even think to offer Doug and Carrie any of it for something such as new appliances they all use and has to be more or less told to give it to them. Doug wants him out of the house for these reasons but Carrie defends Arthur, claiming he isn't that bad (which is odd, as it has been firmly established that Arthur was a terrible father).
An intentional example with Zezelryk. He's a Squishy Wizard, with the caveat that he is so inept that we never have seen him actually performingFunctional Magic, despite repeatedly trying. Because of this, he is far from one of the annoying examples of the trope, especially since he actually does come in useful once in a blue moon.
Loquasto and Bruce are pretty useless too, though Loquasto has some usefulness as the Dumb Muscle. But all three make up for it by having at least one of them be the Only Sane Man when the rest of the group touches the Idiot Ball.
Loquasto's sense of smell and Zezelryk's potion making also occasionally come in handy Plus Zezelryk now has a nifty magic item. Also in the season finale Bruce shows that he's a pretty competent fighter.
Law & Order: Special Victims Unit: A new Crime Scene Unit guy Stucky in the 08-09 season was a load to the detectives, shouting inappropriate things at crime scenes and generally annoying the hell out of the other lab tech and Stabler. All this changed in the season finale when he was revealed to be a complete psychopath who planted evidence and killed a man to "help" the detectives catch a serial killer. And when that failed to impress his colleagues he killed his lab partner and almost killed Stabler. Fortunately Olivia was there to put down the deranged Scrappy.
Charlie was The Load for the first two seasons, but came through in a big way at the end of season 3.
A few characters have occasionally treated Hurley like The Load, but he's likable enough (and also comes through at the end of season 3) that the characterization doesn't stick.
Daniel spent some time as The Load when he was first introduced in season 4 before he gained confidence and moved more towards a leadership role amoung the Frieghties, until midway through season 5 where he suffered a Heroic BSOD after Charlotte died.
And let's not forget Boone, who spent the entire first season being completely useless, then getting a plane dropped on him... while inside it. If you need proof of just how completely worthless he was, his first appearance on the show had Jack sending him off to find a pen to perform a tracheotomy on a woman who did not need a tracheotomy.
Subverted Trope with Merlin. He's the king's clumsy manservant who can't hold a sword to save his life, and yet the Knights of the Round Table all insist on bringing him along on dangerous missions. However, when the Knights turn their backs, Merlin turns out to be an extremely badass mage who has singlehandedly saved all of Camelot multiple times and is the only reason Arthur survives these dangerous missions. Problem is, magic's illegal on pain of death, so no one is aware of this except the audience.
Depending on the Writer, Guinevere. On one hand, her quick mind has proven useful on several occasions, on the other, she's still a relatively small and untrained peasant girl who often winds up being a Distressed Damsel.
The page quote above comes from the end of the episode, Prince of Space. Most of the movie's action involves a group of hapless, middle-aged scientists having to be constantly rescued from Evil Alien Chicken people by the title character. Furthermore, the movie demonstrated a particular peculiarity Japanese children seem to constantly exhibit in movies like this; namely, the need to be within close proximity of the hero at all times, even or especially when he's busy fighting the Monster of the Week, and even or especially when this would put both them and the hero in incredible danger. Maybe it's the Japanese's way of trying to weed out the weak and stupid and keep the population down.
Revolution: In episode 6, Aaron sees himself as such which is why he abandoned his wife—he felt he was only hindering her chances for survival post-blackout.He got better.
The Rifleman: Stars a Bad Assrifle slingingrancher... and his son Mark. When Mark isn't directly getting into trouble himself (and forcing poor Luke to rescue his worthless ass), or getting his father into trouble that he has to bail himself out of, he's probably whining about the school teacher being mean to him.
Robin of Sherwood: Much, the Tagalong Kid from this series, never accomplishes anything, fails as a lookout, and occasionally lets prisoners go. Any fight scene he's in always involves someone rescuing him, even when he gets a Magic Sword. He's quite a liability for a tiny group of constantly hunted outlaws. Of course, he's also the hero's brother... at first. After Robert Huntingdon comes in, they don't even have that excuse. He eventually gets (somewhat) better. At the beginning of the episode "Adam Bell" an entire troop of fully armed and armoured soldiers has a hard time capturing Much, who has only a staff and none of his friends to help. They eventually get him, but he gives them a good run for their money. It says a lot about his Load status that "not getting captured right away" is a point in his favour.
The scientists can't fire a gun to save their lives (literally). While certainly not worthless, McKay redeems himself when something technical has to be done. 90% of time he is the one who saves the day while everybody else just provide covering fire, distraction or just do what they are told. And will be the first to point that out.
Special mention to Dr. Keller. On two separate occasions, Keller ends up in a dangerous situation where she's on the run from the bad guys with one of Sheppard's team (with Teyla in "Missing" and Ronon in "The Lost Tribe".) Both times she is a serious liability, being unable to fire a weapon or fight (and complaining when she has to pick up a gun to defend herself). Granted, the rest of the civilians on Atlantis are Non-Action Guys, but they usually step up their game when the situation calls for it.
Tasha Yar. Her character's complete lack of usefulness is what led Denise Crosby to leave the show near the end of the first season.
In many ways, Deanna Troi filled this role too. She was always being possessed by aliens, abused by aliens in crashed shuttles, abducted by aliens for political gambits, being nearly forced to marry an alien, having her psychic powers robbed by aliens, suffering nightmares at the hands of aliens, forced to listen to a virtual music box in her head for days by an alien, the list goes on. Her only real use on the show was to counsel the random crew member of the week and to tell Picard when she sensed weird things happening while on the bridge. Maybe this makes her closer to Butt Monkey. Troi did manage to Take a Level in Badass during a two-episode arc where she was sent to spy on the Romulans... but left that level somewhere for the rest of the series, never to be seen again. Those episodes are the reason A Day in the Limelight used to be named "Good Troi Episode".
The sad thing is that Deanna had the potential to be useful however the writers always made her conveniently absent whenever her Betazoid abilities would have come in handy. There were a couple of instances when the crew made contact with an obviously deceptive alien race or leader. Deanna could have sensed their deceptive nature and warned the crew but she always managed to be suspiciously absent for those meetings.
In the Supernatural episode "What Is And What Should Never Be" (S02, Ep20), Sam in the Wishverse is pretty useless at the warehouse. At one point he gasps in disgust when he sees the djinn drinking the blood of its victim despite Dean's admonishment to keep his mouth shut and almost reveals their location to the djinn. This is one of the contrasts between Wishverse!Sam and real Sam.
Survivor: Some players are weak in challenges, lazy at camp, and have no real sense of strategy. These are usually the first tribe members to be voted out — if the tribe is playing intelligently. But, since anything can happen in Survivor, sometimes these players make it all the way to the end of the game and even win. Pretending to be this, as Natalie White did, can protect a player against a You Have Outlived Your Usefulness.
The Walking Dead: In the TV series version, Carl Grimes and Sophia Peletier are about as much help as you'd expect a pair of gradeschool kids with a fondness for wandering off to be in the middle of a Zombie Apocalypse — and that's in season 1. In season 2, they actually take a level in being the load; Sophia panics when she gets attacked by a pair of walkers in the first episode, which is understandable, but then she leaves the safe place that Rick tells her to hide in and runs off while he's busy drawing away and killing them — this results in her death when a walker in the woods gets her, and directly leads to every bad thing that happens in the season. Carl gets shot while out looking for Sophia; this prompts the guilty shooter, Otis, to make a dangerous run to an infested highschool with Shane and wind up being shot to serve as live bait for the walkers. Then, after he finally gets better, he steals a gun and wanders off in a tantrum for telling Sophia's grieving mother that there is no heaven — when he finds a walker stuck in the mud, he taunts the thing, and then panics when it manages to escape, running back to the farm. Not only does this lead the undead monster there, he refuses to admit he saw a walker in close proximity and that it may have followed him because he's afraid of getting in trouble. This makes him the indirect cause of the death of Dale, the Cool Old GuyTeam Dad — and earned a lot of bile from the watchers.
Season 3 averts this by showing that the months spent trying to survive have turned the group into a precision zombie killing machine. Everyone pulls their weight and Carl becomes a coldly proficient zombie killer. In season 4 Carol teaches the children how to kill zombies so they can protect themselves without the the help of the adults. The group also makes sure to interrogate any new survivors they encounter to make sure that they can pull their weight if they are invited to join the group.
3rd Rock from the Sun: Harry Solomon. Although all the aliens are often Too Dumb to Live, Harry is the worst. At first he seems to have no official role in the unit, until it's revealed that he has a massive transmission device in his head, and to make space for it they gave him only half a brain. An unusual case because although he's generally useless, he's one of the most beloved and endearing characters in the show.