Villainous Valor

This is one method for avoiding doldrums from having a Boring Invincible Hero. Scenes of Villainous Valor show the antagonists to be outmatched, forcing them to rely on daring, cunning, skill and determination to hold their own against the heroes, or at least go out with a little dignity. They sometimes even continue a hopeless battle for higher reasons than spite! This often results in a tense back-and-forth as the heroes' raw power is set against the villains' measures.

Sometimes they win, sometimes they lose, but the mark of Villainous Valor is that it sees the "bad guys" using Tropes that you wouldn't expect from them. In fact, if you were just tuning in, you might even be confused about who you're expected to root for. Is it the unstoppable White Knight, or the desperately overwhelmed warrior studded with Spikes of Villainy bravely holding him back? Even if you know who's on what side, you might find yourself pulling for the little guy anyway, hoping to see the hero brought down a peg.

This often appears in shows where the villains are sympathetic or the heroes questionable.

Anime and Manga

 * In the early engagements against the Combat Cyborgs in Magical Girl Lyrical Nanoha Strikers, we're presented with a small group of specialists carrying out a daring mission against a whole world full of mages led by a pair of warriors who could mop the floor with them in a straight fight. (The Numbers who can stand up to Fate and Nanoha are introduced later.) Nevertheless, through a series of hair-raising encounters and desperate escapes, they finally win through and make off with the MacGuffin.
 * This appears many times in the Gundam series. Of course, given the nature of the universe, it makes sense.
 * Several versions feature enemy aces piloting machines that are no match for the Gundams, but able to hold their own thanks to superior skill.
 * The early parts of Gundam00 have this in spades, as the pilots of Celestial Being crash around invincibly and the rest of the world scrambles to keep up. You even see mooks making Heroic Sacrifices.
 * Fights in Hellsing are often shown more from the villains' perspective, and we get to see their horror/resolve while Alucard goes One-Winged Angel and cackles like a madman. You may even feel a whisper of sympathy for the Nazi Vampires as a SR-71 Blackbird crashes down on their heads and a shadowy Eldritch Abomination bursts out of the flames to destroy them.
 * In the magical world arc of Mahou Sensei Negima, a quartet of magical bounty hunters lay a trap for some of his students. Negi shows up, and gets to show off how scary powerful he has become. We get to see just how scary he is to the bounty hunters because we're privy to their thoughts.
 * Take a look at the opening scene of the third Inuyasha movie. Setsunano Takemaru, a normal samurai with a simple sword, charges into a flaming castle missing one of his arms to confront a powerful Demon Lord wielding freakin' Sounga.  He was unquestionably a wretched punk who deserved everything that was coming to him, but damn.

Comic Books

 * Given that Superman is practically the poster boy for the Boring Invincible Hero (at least according to some) and his arch-nemesis is an unpowered human, it would be a shock if this never happened in his stories.
 * It doesn't, mainly because Clark doesn't have an ego and Luthor does. So despite the power difference all of Luthor's claims that he's fighting for humanity fall flat due to him considering himself above humanity more than Clark does.

Film

 * A version of this is present in, of all things, A League of Their Own. Where the younger, less talented sister, is pitted up against Geena Davis' star pitcher. She plays the final match through waves of intense determination, and ends up crying at one point. That's how much she wants to win.
 * In the film United 93 the youngest terrorist (who looks about 14) puts up a disturbingly valiant fight when he’s rushed by half the plane’s passengers at the end of the film.
 * In Scanners, you can't help but admire Revok's escape from the ConSec headquarters after he assassinates their last scanner. It gets even more impressive when you realize that as the head of a major scanner underground, he could have sent in underlings, but no, this was something he had to do himself.  Also, toward the end of the movie, it's The Hero who pulls the Not So Different card instead of the villain.
 * In the movie Five Minutes To Live, the evil gangster played by Johnny Cash takes a hostage (six year-old Ron Howard) in order to escape from the police. He quietly tells Ron that he has nothing to fear; Johnny would never kill a kid.  When this doesn't stop the police from shooting at him, he's outraged, and you can't help but agree with him.

Literature
"Dr. Livesay: I can almost find it in my heart to hope he makes it."
 * In the The Lord of the Rings: Return of the King the Haradrim troops keep fighting after Sauron's defeat, and the author comments how they are brave and noble warriors who just happen to be on the evil side of the fence.
 * There's a great scene in Treasure Island where the pirates all want the map that they think Jim has, which he doesn't. Long John Silver picked the map from Jim's pocket, but he allows the other pirates to go on thinking that Jim knows where it is, because as long as he's the only one who knows where it is, they can't hurt him.
 * There's another bit at the end, where Long John knows his chances of escape will be improved greatly if he shoots Jim in the head, but he can't bring himself to do it. Jim, unwilling to use John's mercy against him, helps him escape anyway.

Live-Action TV

 * Buffy the Vampire Slayer:
 * Almost certainly the reason for Spike's early popularity, being simultaneously the first vampire adversary of Buffy to be depicted as more than a soul-less monster, and the first to avoid the Curb Stomp Battles that were endemic in season one. Likewise, it's hard not to feel kinda happy for the random vampire mook who hands Buffy a lucky defeat in "Fool For Love".
 * The Mayor, the Big Bad of season three, and the Man Behind the Man regarding almost every other villain on the series. An Affably Evil Neat Freak, he often stresses the importance of good hygeine, a balanced diet, table manners, and etiquette, with the strongest thing he ever drinks being root beer. Plus he's a big fan of The Family Circus (but not Marmaduke). He'd probably be the ideal elected official had he not built Sunnydale to act as a larder for demons in preparation for an infernal invasion.
 * On shows such as COPS and World's Wildest Police Videos, there will sometimes be a perp who leads the police on a bit of a chase... No matter what terrible thing they may be accused of doing, considering the Can't Get Away with Nuthin' the shows are (rightfully) based on, there will still be a small part of your brain that wants to root for them.
 * Hilary Briss on The League of Gentlemen. Creepy as hell though he may be, he's presented as the Villain Protagonist of his own arc, and you sort of want him to escape.

Professional Wrestling

 * Most Heels who face HHH or the Undertaker. In general, this applies to whenever a beloved mid-carder with perceived superior skills goes up against an opponent they could not legitimately be expected to defeat for story reasons.

Puppet Shows

 * On Muppets Tonight, Big Bad Carl is a monster whose acts usually end with him eating another Muppet. Still, when this results in the crowd applauding (and it usually does) he acts like a typical performer should, bowing and saying, "Thank you! Thank you!"

Tabletop Games

 * Through the Imperium is most often presented as crumbling, it is still the most powerful faction in 40k. In stories set from the 'Evil' faction's POV, we can often see just how much firepower the Imperials can bring to bear against them. And the fact that it's a Crapsack Galaxy for them too.

Web Comics

 * In Cheshire Crossing, The Wicked Witch Of The West repeatedly faces off against Mary Poppins. Poppins is depicted as a stern, overpowered witch who flattens her opponents with brute force, and shows off in both magical matters and mundane with little flourishes that let others know just how totally in charge she is. The Witch of the West on the other hand is made out to be a bitter underdog, defeated before at least once, who spends her time in search of arcane secrets and power sources. When they encounter each other for the first time while in Oz, Poppins is able to knock the Witch of the West around until the Witch of the West gets the drop on her with a bucket of water. Oz has special rules, and Poppins hasn't done her homework.

Western Animation
"Mr. Toad: Boss, it's the Bat-guy! Professor Pyg: It's Batman, Toad, remember, respect our enemies."
 * We often see Brock Sampson from the henchmen's point of view in The Venture Brothers.
 * DC Super Hero Girls; used as a joke in the two part episode "#TheFreshPrincessOfRenFair", Ember is a dragon disguised as a human who is working as a vendor at a Renaissance Fair, highly implying that she got the job hoping her favored prey - princesses - would show up (and she's upset that all she's found are princess cosplayers). She thinks she's gotten her wish with Dee, but her attempt to capture her is cut short when she realizes she has a customer to handle - once she does, she makes sure to lock up and put the "Closed" label up before resuming the pursuit.
 * In the first episode of Beware the Batman, a high-speed chase ensues with the hero - in the Batmobile, of course - pursuing Professor Pyg and Mr. Toad: