The Beast from Beauty and the Beast (not the Disney version) tells Beauty that if she doesn't return to him within a set amount of time, he'll literally die of grief. When she stays just one day later, she receives a vision of him on the verge of death and rushes back to his side, at which point he promptly begins getting better even before she breaks his curse by agreeing to marry him.
Rosethorn is this for her student, Briar, in Circle of Magic. As of Battle Magic, it's clear that he is one for her as well: she very nearly breaks down completely when she realises that he's been injured. Although she's generally better at hiding it.
The Dresden Files has a supernatural variation: White Court vampireThomas Raith has a girlfriend who is schizophrenic and prone to dangerous mood swings. By feeding off her excess emotions, he allows her to be fully functional without the side-effects of medication. When separated from him for too long, her emotional instability returns and she becomes dangerous to herself and others. After Thomas becomes unable to feed off her or even touch her after a mutual Act of True Love, she eventually finds new medications that help her maintain a more healthy emotional state.
Harry himself has his circle of friends that act as a stabilizing influence in his life, but especially the women he's romantically interested in and possibly Ebenezar McCoy. It's been proven multiple times that if they get hurt (or if they hurt him) he becomes...slightly less than stable. Gets turned Up to Eleven post-Changes, because he has to keep them around to combat the Winter Mantle's pull.
In Forbidden, Lochan and Maya are this to each other.
Only with Maya can I really be myself. We share the burden together and she is always on my side, by my side. I don’t want to need her, to depend on her, but I do, I really do.
Diana is this to Caine in HUNGER, to the extent that when Caine thinks Diana is dead he actually asks his brother to kill him.
As the books go on however, she mellows into a less influential crutch, and eventually in PLAGUE, Caine spends an entire book kicking the morality pet.
Herald-Trainee Tylendel, to Vanyel, in The Last Herald-Mage trilogy. He becomes Van's first and greatest love and the only one he can trust. 'Lendel does nothing to discourage this dependence, which is why things start to go south when his own sanity begins to slip. And then it gets worse...
On the other hand, there are milder examples in some Lifebonded pairs, where a Herald with a slightly broody personality and a strong Gift bonds with another who is less Gifted but more stable, and this is treated as a good thing.
I don't know when I've felt so rotten. Somehow I found myself moving about the room softly, as if there had been a death in the family. If I had anybody to talk to I should have talked in a whisper; in fact, when the telephone-bell rang I answered in such a sad, hushed voice that the fellow at the other end of the wire said "Halloa!" five times, thinking he hadn't got me.
In The Mortal Instruments, Stephen Herondale was implied to be this to his second wife Celine, to the point of her nearly committing suicide upon hearing of his death.
In Twilight, Jacob is this, very much, to Bella during most of New Moon. In fact, ever since falling in love, Edward and Bella have generally been this for each other.
Archie Goodwin functions as something like this for Nero Wolfe; as Wolfe's personal assistant, Archie's pretty much the only reason Wolfe's carefully structured life functions as smoothly as it does, but he's also Wolfe's conscience when he feels Wolfe has crossed the line, and his snarky attitude works to motivate Wolfe into accepting work despite his laziness, preventing him from stagnating. Accordingly, despite the frequent tension between them Archie is one of the only people—if not the only person—Wolfe ever expresses any genuine regard for.
To a lesser extent, Wolfe also returns the favour for Archie; most notably, in one novel Wolfe disappears without trace for several months, forcing Archie to open his own detective agency. He makes a point of noting that while he made more money than he ever made working for Wolfe, he found the work a lot less interesting.
In the Novelization of Revenge of the Sith, Obi-Wan and Padme are both this to Anakin, to a point. A point which diminishes steadily as the story progresses and he turns increasingly to Palpatine; even at the beginning, he saw and sometimes resented their influence. Without them—after he kills Padme and drives Obi-Wan irrevocably away—he turns into Darth Vader.
The protagonists mother in The Skin I'm In had her husband as her emotional crutch. When he died she was absolutely miserable.
Lucie in A Tale of Two Cities is the only thing between her father and solitary-confinement-induced insanity. He soon progresses from needing her presence to simply needing her happiness, but when Charles falls under the shadow of the guillotine, that kind of backfires.
Karan of The Three Worlds Cycle has an excuse for this—half-breed characters in this setting are prone to serious psychological issues, and as a Heinz Hybrid she shouldn't even be functional. Her friend/love interest Llian somehow manages to stabilize her, and when she's separated from him, things go badly, to say the least.
In The Two Princesses of Bamarre, Addie is easily frightened and depends on Meryl to protect and calm her. She grows out of it when she has to save Meryl from the Gray Death.
Cathy was this for Heathcliff growing up amidst the abuse and prejudice of Wuthering Heights.
Played very strangely in Lurlene McDaniel's Don't Die, My Love. Luke Muldenhower's the one with terminal cancer, but his girlfriend Julie is the one who clings to him and their relationship as her reason for living. When he dies, she pretty much shuts down emotionally and it takes a group effort to pull her out of it.
In Les Misérables, Cosette is this to Jean Valjean. She's his only source of love and happiness, and when he's separated from her at the end of the novel, he wastes away and dies of grief.
In The Machineries of Empire, while not technically living, Jedao seems to have taken it upon himself to keep Cheris mentally stable in face of War Is Hell, and pulls her out from the edge of a mental breakdown several times.