Heroic Fatigue

Exactly What It Says On the Tin, this is a trope where The Hero, suffering (or enjoying, depending on the mood of the story) from Chronic Hero Syndrome, spends so much of his time and effort helping people, that it is physically and emotionally wearing him down to the breaking point. It can be even worse for him if he has something akin to super hearing or telepathy, so he can always hear people calling for help, even when he's trying to get an hour or two of sleep before clocking in for his Stock Super hero Day Job and chugging coffee for the entire day.

This may lead sooner or later to Passing the Torch and Retired Badass, or in more cynical works, a Heroic BSOD or a Despair Event Horizon, as the increasingly strung-out and hopeless hero just loses it because he can't save all those people who need him. This could of course apply to the villain, for many of the same reasons (well, presumably not the strain of constantly having to save people, but certainly the stresses of dealing with the superheros and law enforcement would be an issue)

Film

 * Daredevil: We see the hero going through his before-bed routine, getting everything put away in just the right place, climbing into the sound-proof casket (necessary due to his super hearing), only for him to hear a woman somewhere nearby crying for help. He only lets out an exhausted sigh before slowly closing the casket to close out the sound.
 * In Megamind,

Literature

 * Harry Dresden goes through this all the time. Often he will forget to eat, or sleep when he's on a case and the world needs saving from supernatural doom. By the time he manages to solve everything he's usually so strung out that he often ends up just blacking out from exhaustion.
 * Alaric Morgan is particularly prone to this in regards his Deryni powers. He is apt to use use his powers literally to the point of falling over at times, unless he he is prevented from doing so. Kelson scolds him for it in The King's Justice, and Azim forbids him from helping with  after he and Dhugal have just spent themselves Healing   in King Kelson's Bride.
 * The Curse of Chalion: Poor Cazaril! To list all his tribulations would be a massive wall of text, but to sum up: in the novel, he rides 800 miles on horseback with a demon-infested tumor in his stomach. Before the novel takes place, he holds a fortress against an extended seige, and the starvation and disease that go along with that. Then he's sold into slavery aboard a galley, where he nearly dies to save Chekhov's Oarman. By the end of the novel he has literally almost hero'ed himself to death.
 * The protagonist of Beachwalker develops a bad case of this partway through the book as she tries to juggle treating her patient, surviving the aftermath of an earthquake, and  all at the same time.

Live Action Television

 * In Heroes season 4, Peter wore himself to the breaking point trying to rescue and heal people in his job as a paramedic using his abilities.
 * In an episode of Lois and Clark, Lois was near the breaking point when she realized that even with all of Superman's (borrowed) powers, she could not save everyone.
 * In "The Listener" this turns out to be a plot point. Toby will

Tabletop Games

 * In the Pathfinder Adventure Path Curse of the Crimson Throne, most descriptions of Field Marshal Cressida Kroft--the captain of the city guard and resident Reasonable Authority Figure--stress how exhausted she looks from dealing with the various disasters of the city.

Video Games

 * By Mass Effect 3, Commander Shepard really starts getting hit with this and by the end of the game, even before the final battle, s/he sounds completely exhausted and spent.

Web Original
""I'm very tired.""
 * Sailor Nothing has a nasty case of this, to the point of her being constantly on the verge of a complete breakdown. Doesn't help that she gets splitting headaches every time a Yamiko is created, and goes out to fight even when she's badly injured.

Western Animation

 * Batman suffers an emotional breakdown like this in the Batman the Animated Series episode "I am the Night".
 * J'onn J'onzz temporarily quits the Justice League late in the third season of Justice League Unlimited partly due to this.