The Soulsaver

A character who saves souls from some kind of literal or symbolic hell/limbo. The character might be a preacher, psychologist, psychic or whatever, depending on the setting. In some cases and settings, the saving requires some time and afterthought. In others, a Epiphany Therapy is available.

May or may not be a Heaven Seeker: The saving means peace, closure, and often some kind of good life - but it can be either in this life or in some afterlife or release.

A religious version of The Soulsaver is different from a Soulsaving Crusader by not using such harsh methods.

Anime and Manga

 * The exorcists in D Gray Man, especially Allen. The akuma they're fighting are powered by the souls of the dead, and unless they're destroyed using Innocence, they disappear instead of being redeemed. Some of the organization is a lot more focused on destroying Akuma than saving their souls, though.
 * When the Soul Reapers from Bleach destroy a Hollow, they allow its soul to pass on to the Soul Society, so that their souls can later be reborn. Quincys, however, are the antitheses of this trope - when they destroy a Hollow they destroy the soul, too.
 * Puella Magi Madoka Magica -

Comic Books

 * In Chick Tracts, any christian can save lost souls from certain damnation, casting out evil spirits along the way.
 * The fourth and fifth book of Sandman revolves around this trope. The fourth being Season of Mist, with Morpheus trying to save his lover from Hell. Not out of love, however, but due to guilt and the realization that he messed up. He had condemned her to hell quite some time ago because she refused his marriage proposal. In terms of moral improvement, he saved (or at least improved) himself.
 * In the fifth book, A Game Of You, most of the main characters try to save the protagonist's mind from remaining artificially stuck in a dream. It doesn't work out very well.

Film

 * In The Sixth Sense, a human and a ghost do this to each other. It is implied that the human goes on to save more lost souls from their limbo.
 * Poltergeist. The psychic Tangina helps a group of ghosts (lost souls) trapped in the astral plane go into the Light.

Literature

 * Larry Niven and Jerry Pournelle's SF novel Inferno. Benito Mussolini tries to save the souls of people in Hell by helping them escape. At the end of the novel Allan Carpentier takes over his role.
 * According to The Bible Jesus dying on the cross saved the souls of all who believe in Him, both those who had died before Him like Abraham and people who came after Him. (Some interpretations have him literally going To Hell and Back to retrieve the righteous dead.)
 * In the original Dracula, the vampire-hunting protagonists are said to be saving the souls of the undead from a presumably rather uncomfortable state of limbo.
 * Lyra and her daemon, Pan, in His Dark Materials. She sets free the severed daemons of Bolvangar, and even better, saves the rest of the children from that same fate. It turns out
 * Part of the Abhorsen's job description: sending the souls of the recently departed swiftly down the river of Death, and putting the walking Dead to rest again.
 * This is the purpose of the Knights of the Cross in The Dresden Files. They will fight people who succumb to Demonic Possession and kill them if necessary, but if they surrender, throw their demonic powers away, and show a desire to atone and repent the Knights are oath-bound to help them with it (even if they're not genuine about it).

Live Action TV

 * Ghost Whisperer goes around helping ghosts resolve their conflicts and send them into the light.

Video Games

 * In World of Warcraft A'dal appears to save a dying crusader from being transformed into one of the Scourge by sending his soul directly to the Light.
 * In Dantes Inferno, the player can absolve damned historical figures, normal souls and demons, thus releasing them from Hell, and earning holy experience points in the process.

Web Comics

 * One part of a Medium's job in Gunnerkrigg Court is helping those who "stuck" after death and before afterlife, and are inaccessible to Psychopomps, so only mortals can deal with them. Unlike "normal" ghosts (aware of both visible and invisible world and having their own niche), "stuck" people indefinitely exist half in reality, half in their own nightmares and as such aren't easy to approach even in the best circumstances.

Web Games

 * In Echo Bazaar, an optional subplot leads to your character becoming one of these, literally rescuing people's Soul Jars from devils.