Most of the things that come to my mind, are probably what would immediately come to your mind.
Laconic:1. Gods. There's a god that is keeper of souls/ruler of the underworld that the person must find. And either A: Convince the god, or B: Just take the soul back.
2. Objects. Often provided with no backstory (1-up). Objects to revive that dead that DO have backstories are usually made from some (rare) creature (that is impossible to find/catch and possibly extinct).
3. Sacrifice. May overlap with gods. But one must give a life to bring one back.
Verbose:The legend of Orpheus and Eurydice is a legend that would fall under gods.
Wikipedia quote:
After his music softened the hearts of Hades and Persephone, his singing so sweet that even the Erinyes wept, he was allowed to take her back to the world of the living. In another version, Orpheus played his lyre to put Cerberus, the guardian of Hades, to sleep, after which Eurydice was allowed to return with Orpheus to the world of the living. Either way, the condition was attached that he must walk in front of her and not look back until both had reached the upper world. However, just as they reached the portals of Hades and daylight, he could not help but turn around to gaze on her face, and Eurydice vanished back into the Underworld. When Orpheus was later killed by the Maenads on Dionysus' orders, his soul ended up in the Underworld where he was reunited with Eurydice.
Though he failed... you can get how he would have succeeded. Although there is already a game based on this myth called
Don't Look Back. There are numerous similar myths to this one, too. (Lover quests to world of dead to rescue soulmate's soul)
Other ways to use gods might be that a god is in distress and if the hero manages to save him/her he can use the god's power. Or the hero must find a way to blackmail the god.
Next up is objects. The quest is for an object that will bring back a dead person. As said above, often named for/from a creature that comes back from the dead. Take a Phoenix Down from Final Fantasy. Named so for the Phoenix which comes back to life after its death. Your quest could to find and kill some mythical creature that rises from the dead, or just find the elixir from someone else who has already done so.
For a REAL animal you could make something up from, try the Immortal Jellyfish.
http://en.wikipedia.org/wiki/Turritopsis_nutricula It can revert to a time before it's sexually mature, and can supposedly do it again and again and again. Though... I suppose it's closer to immortality than bringing a dead thing back to life.
No elaboration on sacrifice, since that's pretty common.
Take your pick. Usually people get more creative with the "gotchas" of reviving a person (Orpheus can't look back, the revived person is only a body with no soul and so unhappy they want to kill themselves etc.) than the actual reviving. If that's the sort of thing you'd like to know more about, I
may have a bit more to write.
I don't know if you want an adventure game (quest to underworld is better for that genre), mystery/visual novel game (find a way to blackmail a god might be good for this genre), or something else entirely. In fact, this person trying to revive his wife might be a very small part of your game and not the main quest.
Anyway... I'm trying to work not being so wordy on forums, so that's all I've got for now. Interesting topic, however.
