The gods of A Moment of Peace, are a rare example of peaceful, useful emotion eaters that have a symbiotic relationship with the mortals they feed off of. They eat gruel made of human sorrow and baked cheer, and in return answer prayers and perform metaphysical chores that benefit humanity.
The 'cubi in Dan and Mab's Furry Adventures feed this way, with each demon usually having a favorite "flavor" that's more filling for them. It doesn't remove the target's emotion, though, they're sustained just by being around someone who's emitting emotion. Although it's common practice for them to provoke the emotion they want through non-supernatural means.
For example, one who feeds best on Anxiety might take up a job in a waiting room, allowing them to feed on the patients while earning their paycheck.
In Megatokyo, it's suggested that the magical girls gain their power from the emotions of other people and are compelled to cause said emotions. What exact emotions seems to depend on the particular girl.
The Demoness in Yosh! Stated by other characters to likely not actually need emotion to survive, but that it does fuel her powers.
Walter from Wonder Mark#548 has a nutritional deficiency with this requirement.
Slake from Fans! claims to be an emotion eater, but it's not clear if he really is, or just a Vampire Vannabe.
Every Cubi feeds of a different emotion in Project Future, a fancomic of Dan and Mab's Furry Adventures (above).
One of the characters in the later chapter was brought Back from the Dead as an android was Cubi who fed on Surprise
It also mentioned that there have been Cubis who fed on Fear, Joy, Depression, etc.
Daniel is a vampire that drinks blood to feel life, and that includes the emotions that go with it.
In Alice and the Nightmare, everything is powered by energy harvested from dreams of Earth people. As harmful as it might be to the minds of small children, most of the danger is on Wonderland's side; children don't have the mental control to fight their fears, which promptly manifest as hulking murder-monsters and hunt down the invading Wonderlanders.
One Oglaf strip introduces a wraith-thing that feeds on fear. Notably, because it actually eats fear, its victim is left a Fearless Fool, and promptly gets himself killed screwing around with a crocodile. The wraith muses that it should feel guilty about that, but for some reason it doesn't. Cue another wraith appearing, announcing that it feeds on regret.
Cucumber Quest: The Nightmare Knight is literally powered by fear; as long as the people of Dreamside are scared of him, his magic is ludicrously powerful and hes nigh unstoppable, hence why hes so obsessed with maintaining his reputation as The Dreaded. His minions/children, the Diaster Masters, are also technically this, as he created them using said fear-based magic. This gives him even more motivation to keep being a villain, as hes scared that if he stops, theyll die.
After Aurora introduced light (and with it, the emotional spectrum) onto the world in the Magical BoyCreation Myth, Devoid discovered a dark-based by-product of this light born from negative emotions and that feeding on this darkness made him stronger. His minions are also able to feed on this darkness as well, growing bigger and stronger the more they feed off of humans.