Forgot to Gag Him

What is this wizard we captured murmuring under his nose?

—reportedly a role-playing game quote

At long last, Captain Superhero has been captured by your clever traps! His superpowers are entirely nullified, and he's tied up with specially-prepared Unobtainium-bonds that you know for a fact that he couldn't break even if he got his powers back somehow. He's completely immobilized and helpless! Heck, you'd Just Shoot Him if it wasn't for certain unavoidable, external factors...

...what, GAG him? That's a touch too kinky. Wouldn't want people to get a Foe Yay vibe here, would we? And it's not like he can cast spells or unleash destructive, supersonic yells or anything like that. All he can do is talk. Heck, maybe listening to him ranting about your evil deeds or begging for his life could be kinda' fun.

Although... what he's saying sorta' makes sense... and your most faithful retainer seems to be spending a lot of time listening to him, for some reason... well, what's the worst that could happen, really?

Basically, this is a situation where the hero's been captured and immobilized, but he's still got the use of his mouth, and proceeds to talk his way out of trouble. What, exactly, this involves varies. It could be a Batman Gambit, providing the villain or his minions with just the right information (fake or not) that you know will push them into doing just what you want them to - or you could play on whatever fears and concerns they may have to bluff your way out. Alternately, you could appeal to their better nature, reminding them that Even Evil Has Standards, perhaps prompting a Heel Face Turn or Mook Face Turn. Whisper sweet, honeyed words to both the villain and his henchmen to provoke an Enemy Civil War. Or maybe you could just bribe The Dragon or some of the other Mooks into helping you out...

Either way, a lot of trouble could've been avoided if the villain had just thought to gag him.

Compare Talking Your Way Out, which is different because—actually, how is it different?

Compare Hannibal Lecture, when someone is taken captive with the intention of being broken through interrogation, only to break their captor instead.

Examples of Forgot to Gag Him include:

Comic Books

Empowered: Our heroine finds herself in this position quite a lot, though she sometimes accidentally reminds the baddies to apply a gag.

Literature

Lyra Silvertongue from His Dark Materials got her nickname by pulling this off - after being captured by the armored bears, she manages to ingratiate herself with them, luring their leader into a false sense of confidence, ultimately leading to his downfall in a duel.
Miles from Vorkosigan Saga manages to Heel Face Turn so many people with his sheer gift of the gab that one Admiral qualifies for 'Dangerously Genre Savvy' solely by virtue of instructing his men to cut out his tongue if he tries to speak. And it still doesn't save him from getting talked into turning sides later...
Both averted and played straight in Dune. When Lady Jessica and Paul are captured by the Harkonnens she is gagged so she can't use her Bene Gesserit Voice ability on them. Unfortunately for the Harkonnens guarding them, Paul also knows how to use Voice.
Plato's Republic (making this Older Than Dirt) begins with an account of Polemarchus insisting that Socrates accept his hospitality—giving him the choice of remaining voluntarily or having Polemarchus and his friends detain him by force. When Socrates asks if he might persuade them to let him go, Polemarchus replies that they will simply refuse to listen to anything he has to say.
Dominic Flandry in "Tiger by the Tail." The Scothani kidnapped him in the belief that he was an incompetent "secret" agent, but had access to information they wanted for their limited war on the Terran Empire. By the time Imperial forces arrived, he'd talked the Scothani alliance into an Enemy Civil War which the Imperials easily mopped up.

Live Action TV

Dr. Mark Sloan in Diagnosis: Murder - when kidnapped by the insane children of a Mad Bomber he got sent to the electric chair, he manages to play them against each other, while secretly sending clues to his partners-in-crimesolving, leading to his inevitable rescue. One of the agents on the case even comments that they really should've shot him right away...

Web Comics

In The Order of the Stick, at one point the party's rogue manages to talk down some bandits by pointing out the economic issues with their chosen profession. Averted when the order is dragged off to face trial in Azure City in chains. Miko has the sense to gag Vaarsuvius.

Western Animation

Batman has been known to use this approach whenever he turns out to be not QUITE Crazy Prepared enough. This includes that time in the Justice League cartoon when he prevented Harley Quinn from killing him by playing on her insecurities and her affection for The Joker, and when he was caught by the Injustice Guild, and proceeds to (overtly) seduce one member of the crew while (covertly) bribing another.
In My Little Pony Friendship Is Magic, Rarity is captured by creatures who want to use her gem finding powers for their own purposes. She turns the tables by whining so obnoxiously through the whole thing that at one point they even agree to work for her just to get her to stop, and are desperate to get rid of her by the end.