I Dream of Jeannie: Two third season episodes see Majors Nelson and Healey fall under the control of tough (and insane) officers who run them through unbelievably tough exercises.
Angel: Connor. Training from Hell in a very literal sense — he was raised in a hell dimension by a vengeful vampire hunter who was training him to kill his vampire father.
One thing that's specifically mentioned is tying 7 year old Connor to a tree and leaving, expecting the child to free himself and then track his adopted father across said hell-dimension until he caught up with him (which he did). Angel is understandably horrified when he hears about this.
The Colbert Report: This basically sums up the "Colbert-cisers", a pair of parody exercise shoes presented. The left shoe has a six inch heel ending in a greased marble, which supposedly improves balance, while the right's patented "Cindersole" builds ankle mass. Imagine walking in those.
Extreme Weight Loss: In this reality TV series, the personal trainer subjects all applicants he is interested in to a much shortened version of this, causing 95% of applicants to drop out. He wants to only train the people who are motivated enough to do the strict weight loss regimen, including diet and a LOT of exercise, for a year. And that means pushing people past their limits, which is what he does in the brief Training from Hell.
Farscape: Part of training to be a Peacekeeper, in that the final Prowler pilot training "simulation" kills you if you fail.
Also the whole point of "Mental As Anything" is meant to be this, although compared to what the characters involved have suffered on various past occasions at the hands of their enemies, it's positively gentle.
Heroes: Peter's training to control his powers under the tutelage of Claude involves him being framed for robbery, beaten repeatedly in the face with a stick, and thrown off a skyscaper to his (temporary) death.
Also, in ancient Japan, Hiro made Adam/Kensai fight ninety angry ronin and (in the graphic novels) leaving Adam to fight a very large, angry, mother bear as part of the 'be a samurai' montage.
As is pointed out above, beating someone up with overwhelming force is not usually a good way to train but since Adam can regenerate, and Hiro can pluck him out of trouble, they get away with it.
House: Plays this straight at the beginning of Season four where several applicants are subjected to various (often cruel, degrading, or downright ridiculous) tasks in order to seize one spot in House's diagnostic team. Moreover, House arguably does this all the time with the members of his team — training and pushing them constantly, to be their best at all times. Basically, he teaches them how to be a doctor — only, he teaches them how to be a doctor like him. Deciding if this is a good or a bad thing is up to the viewer. Cuddy most certainly doesn't like it.
Kamen Rider is a notable Trope Codifier in Japan and actually influenced many of the modern Japanese shows. The heroes had to go through many intense trainings under their friend and mentor Tachibana in order to develop new techniques and tactics against the formidable enemies.
No Reservations: Tony and his crew had to go through training with ex-special forces guys to prepare for whatever awaited them in Kurdistan. The fun included how to look for mines with a knitting needle, random first aid "quizzes" with people suddenly screaming in the parking lot, and seeing how useless cinderblock walls are against automatic weapons.
Teen Wolf: Allison is put through this by her father (Chris Argent) and to some degree, her aunt. Both threatened to kill her boyfriend in front of her, leading poor Allison to hysterics, and her father left her tied up and alone to struggle out and untie herself as part of her training, too. When her mother ends up dead (having killed herself because she'd been bitten and she'd rather be dead than turn into a werewolf), Allison is hysterical and asks if this is just another one of her father's sick training exercises. It's not, but the fact that she thought it might be speaks volumes about what kind of off-screen "training" she may have had to endure. And on this show, it's definitely played straight, and she's a master archer and hunter in every way now.
Psych: Shawn's father Henry subjected him to a child-friendly version of this in order to develop his observational and deductive skills, with the intention that Shawn would follow in Henry's footsteps and join the police force. Naturally, seeing as he was just a kid at the time, Shawn grew up to resent this and rebel against Henry's teaching; unfortunately, Henry is a "Well Done, Son!" Guy, and their relationship wasn't exactly cordial as a result.
Actually, in the flashbacks, it looks like Shawn wasn't nearly as resentful of his father as one might expect until Shawn's mother left and Shawn mistakenly assumed it was his father's fault.
Henry considered Easter Egg hunts 'training', and did so by burying the eggs three feet underground. With sharp rocks and broken glass over their burial place. And forced Shawn to search three weeks for the eggs. And is still keeping tabs on how many eggs are still buried (2). Oh, and Shawn was 8 at the time.
Henry also locked Shawn in the trunk of the car when he was around eight years old, just so he could learn how to get out of one. The neighbors watching at the time were understandably disturbed.
Revolution: New conscripts into the Monroe Militia are confined aboard an old ship anchored in the middle of a river and subjected to beatings and psychological pressure until they are molded into proper Mooks. After that, presumably something resembling actual military training begins, although given the performance of the militia in the field one wonders if this regimen is strictly For the Evulz.
Smallville: Lana Lang goes through this between her departure in season seven and return in season eight.
Supernatural: After the murder of his wife by demonic forces, John Winchester raises his sons to be hunters, relentlessly running his boys through safety drills and weapons training, and punishing them severely for failure. It is mentioned that Dean sawed off his first shotgun while in the sixth grade, and that Sam was given a handgun to keep under his pillow.
Surviving The Cut: This Discovery Channel show about real-life special forces training. The most harrowing lesson (in season two's Special Operations Aircraft Rescue episode) wasn't about killing people or overcoming stress but the consequences of losing track of your teammates: The two "captured" men had to stand in front of the unit's MIA-POW monument while the rest of the squad dictated condolence letters to their parents, then lay in a "plank" position to think about how their buddies lives were over.
Tensou Sentai Goseiger: Self-inflicted, where Agri asks his teammates to help him in preparing for a track meet. Most of the ensuing sequences apply, but especially when the Sixth Ranger decides to transform into his Humongous Mecha form to chase Agri all over the field!
UFO: Not an example of training, but more the Psychological Assessment From Hell — after witnessing a Flying Saucer incident Paul Foster is subject to numerous forms of intimidation from SHADO operatives. It later turns out that they were evaluating him for recruitment into their organisation.
Ultraman Leo: Dan Moroboshi puts Gen Otori throught this to make him learn new techniques and defend the Earth better.
Arrow: How is Oliver Queen, Spoiled Brat party-hearty rich kid able to kick so much ass? Five years trapped on an island with an army of merciless killers, some of whom are supers. He had to suffer insane torture (and he still has scar tissue over 20% of his body to prove it) and grieve the loss of many friends, but some of those friends taught him some amazing fighting techniques.
Sara Lance also went through a similar thing, as viewers learn once it is revealed she is still alive - the island combined with The League of Assassins trained her.
Thea Queen between Season 2 and 3 went through 6 months of the same League of Assassins training which included things like having her hands burned repeatedly to learn to endure pain.
Subverted with Laurel Lance, who decides to take over her sister's role as superhero after her death. She notably lacks the Training from Hell the other three go through, just learning boxing and then training with Nyssa who is heir to the League buts let's her stop for milkshakes when she wants. Consequently Laurel's way below the standard of the others. Effective way of showing why Training from Hell is necessary on a super-hero show.
Nikita: Virtually everyone on this show goes through this, as the show is about training people against their will to become insanely skilled assassins. Nikita and Alex are great examples as early on as the pilot.