I Need You Stronger

The Big Bad is sending our hero (and his Ragtag Bunch of Misfits companions) through the wringer. He clearly has the power to wipe them out any time he feels like it. But he's content (for now) with sending out wave after wave of progressively stronger Mooks, Elite Mooks, and the occasional Quirky Miniboss Squad to test our hero. Maybe he's even fought them personally, but let them live, maybe even let them think they beat him. Maybe he even leaves them alone to train for their inevitable confrontation. So why don't they finish the protagonist off and be done with it?

Because it's All Part Of his Evil Plan. Maybe he needs the heroes strong enough to get to the top of Mount Tropey and retrieve the Crown of Trope-Tan. Maybe he needs The Chosen One as strong as possible before he takes his power or body as his own. So he keeps sending out one stronger opponent after another to test Our Hero (or lets him seek them out on his own). After all, if he can't handle that, he's no good for the Master Plan. Or the Big Bad just may be a Blood Knight who wants to beat him at his strongest.

This is a subtrope of Evil Plan. See also: I Let You Win, Not Worth Killing, Bring Him to Me. Often a part of a MacGuffin Delivery Service if the hero is an Unwitting Pawn. Compare Stealth Mentor. Contrast You Will Be Spared.

Examples of I Need You Stronger include:

Anime and Manga

Cell and Vegeta on Dragonball Z took turns with the Blood Knight variant of this trope. Vegeta could've easily destroyed Imperfect Cell (or let Future Trunks do it). But Cell appealed to his Saiyan blood, allowing him the opportunity to absorb Android 18 and achieve full power. Likewise, Perfect Cell could've wiped the Z-Warriors out after this. But his Saiyan blood (since he was created using the DNA of the most powerful warriors, including Goku and Vegeta) caused him to give Goku and company time to train and get stronger, so he could crush them at their best, with the whole world watching.
In Naruto, Itachi decides not to kill Sasuke along with the rest of the Uchiha clan. The reason why he does this changes several times, always somehow related to this. Then it's revealed that the actual reason was that he was Good All Along.
Saiyuki: Journey to West: The Sanzo party travels over land at the request of the Merciful Goddess, in order to be more of a team.
In Bleach, Aizen allows Ichigo to go through one last bout of Training from Hell because he wants him to be stronger when Aizen finally "eats" him. Given how Drunk with Power Aizen is during their later fight, it becomes clear that Aizen just wanted a Worthy Opponent to crush with his new powers. It backfires on him because Ichigo took too many levels of Badass and was actually much stronger than Aizen anticipated.
In Lost Universe, the main villain Yami doesn't kill Kain Blueriver when they first meet, wanting him to be stronger. Making him stronger worked too well.
In Fullmetal Alchemist, this is why Edward Elric and Roy Mustang survive long enough to win, in the manga. Well, Roy at least; Ed is already 'strong enough;' it's just that it's not yet time for the sacrifice.
- Alarmingly, if Roy had caught a bullet during the coup, it would probably have ruined the Big Bad's plans more thoroughly than any of the heroes' actual endeavors.
  - On the other hand, given the way Roy ended up being coerced it looks like they didn't need nearly as high a level in their sacrifices as they tried to obtain—they could have pulled that trick on every alchemist in Central starting with Armstrong, if necessary, until they hit one who survived the Gate.
  - On the other hand, the eclipse window was kind of small.
In Hunter X Hunter, Hisoka is the Blood Knight variant. He just wants to have fun and fight strong opponents, and Gon and Killua look like they could grow up really fun to fight, so he lets them live and encourages their...development. And ogles their butts. Togashi doesn't even try to get crap past the radar, he just throws crap in and goes 'neener neener.'
- This is the guy who cut off his own arm to make a casual fight more interesting. And who had a years-long Plan that involved betraying some of the most dangerous people on earth just to fight their leader. You should have seen his face when a side-effect of relying on Kurapika's vendetta turned out to be that Chrollo Lucifer would die if he used his powers again. Chrollo thought it was pretty funny, himself.
In One Piece, Mihawk spares Zoro's life in their first encounter even though he's a massively inferior fighter. This is because he sees Zoro as having the potential to give him a truly challenging fight once he's traveled the Grand Line. He even goes so far as to personally train Zoro during the timeskip.

Fan Works

In The Games We Play by Ryuugi, a crossover between The Gamer and RWBY, Jaune Arc discovers that the creator of the Grimm, who appears to have known him in a previous life, is helping him increase in power at an accelerated rate despite making it very clear that they are enemies; Jaune speculates that there is something that they need from him that he can only provide once he has "leveled up" sufficiently

Films -- Live-Action

In Star Wars, the Emperor wanted to make Luke Skywalker stronger, eventually making him his right-hand man.
Pai Mei invokes this trope in Kill Bill Vol. 2 while training The Bride; "Since your arm now belongs to me, I want it strong."

Literature

We see a form of this in Harry Potter and the Goblet of Fire where "Mad-Eye Moody nudges and helps Harry along in his Tri-Wizard Tournament challenges, for the sole purpose of luring him into a death trap
In The Pendragon Adventure, This trope is the reason Saint Dane doesn't simply kill all the Travelers. In fact, it's also the reason he even lets Bobby find him in any territory at all. When Saint Dane says he his done with his work in a territory, he means it.

Live-Action TV

In the updated Battlestar Galactica, it's never exactly clear why the Cylons didn't simply Zerg Rush the fleet, destroying Galactica and picking off the rest of the fleet at leisure. After all, they'd wiped out 99% of humanity already. Why tiptoe around killing the rest? It's been suggested (but never spelled out on-screen) that this was Cavil/One's doing: He wanted to prove to the Final Five that Humans Are the Real Monsters and not worth saving (thus justifying his own hatred of the Five and humans) by hounding what was left of the Colonies until they turned on each other (which sort of was the case). The hypocrisy of this was not beneath notice.
In Kaizoku Sentai Gokaiger episode 28, the Monster of the Week is an alien bounty hunter and thrill-seeker who does it twice. In the past, he nearly killed Captain Marvelous but stopped short and even injured himself to create a weak point and taunted Marvelous to come back strong enough to challenge him. Then in the present, he handily defeats Marvelous a second time (mostly due to his being paralyzed by fear) and leaves mid-fight despite being paid to kill the Gokaigers.

Music

The reason a father would name his boy Sue.

Video Games

In Final Fantasy IV, Gobelz can't get into the Sealed Cave himself. Cecil can, but isn't strong enough to get through the deathtraps on his own. Cue the Sorting Algorithm of Evil.
And in Final Fantasy XIII, this is indicated to have been in effect for the first portion of the game. Someone rather high up wants the Pulse l'Cie to get stronger. Turns out it's Primarch Dysley, a.k.a. the fal'Cie Barthandelus, as part of his Thanatos Gambit.
In Golden Sun (both games), Alex does jack squat to help his allies defeat you, as part of a plan to unleash Alchemy on the world. 30 years later, he's STILL at it.
This is the Lich King's plan for the World of Warcraft expansion that bears his name. Allow the player characters to grow stronger and better geared, lure them into Icecrown Citadel, then slaughter them all and turn them into the elite vanguard of his undead armies. Naturally, he fails miserably at the "slaughter them all" part.
- Oh no, he actually quite successfully slaughters the entire raid and one-shots everyone with Frostmourne. Unfortunately instead of finishing off Tirion Fordring himself he instead opts to Evil Gloating as he's attempting to convert the players to Scourge, Tirion summons the powers of Deus Ex Machina and breaks Frostmourne in half as Arthas gets Hoist by His Own Petard of all the souls his sword had consumed and the raid is revived and finishes him off.
In Super Paper Mario Dimentio interferes with the protagonists for this purpose, allowing them to defeat Count Bleck, thus freeing the Chaos Heart for him to use.
In the first Super Robot Wars Original Generation, every villainous organization is like this. In the cases of both the Divine Crusaders and Ingram Prisken, it's obvious that they're Stealth Mentors. The Aerogaters, on the other hand, want the heroes to be as strong as possible for when they're Brainwashed and Crazy.
Played twice in Kingdom Hearts:Birth By Sleep. Master Xehanort encourages Terra to train and strengthen his powers in preparation for stealing his body to cheat death, while Vanitas encourages Ven to become stronger because their powers need to be equal to complete the χ-blade.
Diablo I. Whether it was Diablo's plan or not, it works. Failure Is the Only Option, and that's why he's 10 times stronger in Diablo II.
Blue Dragon. Those LivingShadows you use to fight? They're fragments of Nene's one. He didn't feel like doing his own Level Grinding, so he let you do it for him. He promptly takes the Shadows back when you confront him at the end of Disc 2, revitalising himself and leaving you powerless.
Akuma from Street Fighter seems to imply that he views Ryu in this light. He could easily destroy Ryu but instead lets him live and train, believing that with proper nudging, he will develop the same dark fighting spirit that Akuma embraces. In the UDON Comics series of Street Fighter comics, this is outright stated after Akuma wipes the floor with Ryu and lets him live, leaving him with the trope as his parting words. In the end, this is subverted as Ryu chooses to reject the Dark Hadou and walk a more pure path as a warrior.
In Famous. Kessler could easily have killed Cole any time he liked, if he wanted Cole dead. He doesn't do this, however because he's actually a much older version of Cole from a Bad Future, who's traveled back in time to ensure that Cole gets strong and ruthless enough to beat the opponent Kessler couldn't, and so prevent it from becoming a Bad Future. Kessler shows no such qualms about killing Cole's loved ones, however.
The God King from Infinity Blade subverts this. He never hesitates to impale defeated warriors and absorb their strength with the Infinity Blade. However, he never tries to nip things in the bud by hunting down the warrior's son when he's still a child because he wants a worthy champion to help him fight the other Deathless.

Web Comics

In The Wotch, it's clear that Xaos has enough power to take out Anne or Miranda (possibly both of them at once), as does Kohaine. He's explicitly testing Anne, wanting her to grow as strong as possible before stepping in and stealing her powers. Why he can't just take them now and be done with it...? *shrugs*
In The Order of the Stick, Xykon invokes this trope to Roy, offering to let him go so he could gain a few levels because "good heroes make good villains." Roy decides to fight him anyway. (Xykon then subverts the trope by going ahead and killing Roy. Don't worry: He gets brought back.)
- Later, General Tarquin does it too, letting Elan go even after he's tried to kill him. so he can gain some more levels, finish the current questline, and THEN come back to try again. His reasons are cleverer than most, however - he basically says that, should he lose in a climactic duel against a powerful hero, he'll go down in history as a legendary villain. And if he wins? Then he wins. Of course, the fact that he's Elan's father may also play a role in his decision.
In Our Little Adventure, the Palm Tree Ghost tells Julie that the city of Everwood should be her next destination, but she'd probably want to spend some time gaming a level or three before proceeding there.
A variant on this shows up in Eight Bit Theater, when Sarda reveals that the true purpose of the Light Warriors' questing was to make them as strong as possible, just so they would know that not even that much strength could stop him from killing them.