Fatal Frame/WMG

Each set of twins have repressed incestuous feelings for each other.

Because of the village's beliefs, no set of twins ever had any close friends, except for each other. As they got older, their feeling may have developed into something more, due to simply having no one else to share those feelings with.

• Musubi Osaka tried to admit feelings to another villager, and he said that being involved with twins was something that he couldn't do.
• Possibly Jossed in the case of Ryokan Kurosawa, who married after his ritual. It is possible that he simply moved on after his twin's death, though.
• The person Itsuki loved most, even more than the Kurosawa twins and Chitose, was his brother Mutsuki. In fact, the ritual failed because he loved his brother too much.
  • Not quite. IIRC, part of the ritual is that each twin must have some kind of hidden resentment towards the other. The reason Itsuki and Mutsuki failed was because Itsuki absolutely could not hate anything about his brother (which sort've translates into "loved him too much.")
    • There was never anything in the game that mentioned hidden resentment having a part in the ritual. The reason the Tachibana's ritual failed really was because Itsuki loved Mutsuki too much.
• Sae deliberately fell down a cliff so Yae would come back and be together. Years later, Mayu did the same.
• I'm calling Jossed for the Kiryu twins, simply because I don't want to think about it

Rougetsu Island is also a gateway to hell.

Well the first two games had a gateway to hell, and the third game had the Abyss of the Horizon, which was a crossroads to the spirit world.

Mio is partially possessed by Yae throughout the game.

Yae returned to the village not long after the Darkness broke free. When she saw that it was too late to prevent the village's destruction, her soul tore itself in half with grief. One half kept its memories and remained at the Torii gate, weeping. The other purged its memories out of self-preservation and stayed within Yae's body, later making an appearance in the first game.

Now remember early in the game when Mio finds a crying woman at the village entrance? When Mio touched the spirit's shoulder, she accidentally absorbed it and became possessed on a minor level. For the rest of the game, Yae's spirit whispers into Mio's ear, so to speak, only taking stronger control at the last minute in order to complete the ritual. (If you'd like, contrast Yae's torn half-soul with the vengeful, Darkness-ridden spirit of Sae, which we find is perfectly capable of full-on possession.)

Mio's semi-possession is also why Sae is so intent on strangling Mio; she can sense that part of her long-lost twin is in that body. It also explains the seemingly-miraculous appearance of Yae in the Promise Ending.

The Crimson Butterfly that guides Kei throughout the Manor of Sleep is Mayu.

I've heard this theory before, and I think it's extremely plausible. There's a particular photograph Kei can take that clearly shows that Mayu is in the Manor of Sleep. Kei, however, only ever realizes that Mayu is there once the photo is developed in the waking world--she simply appears as a butterfly to him. If she's there with Mio in butterfly form (though Mio too doesn't realize it), it would make perfect sense for her to also be the helpful butterfly that Kei encounters.

The Good Ending of FFIII is the true ending.

In the previous two games, to obtain the Good ending you merely need to complete the game on a harder mode without any other changes to the gameplay experience. But the third installment is different, and requires that Kei perform a side-quest in a New Game Plus. Unlike in any other game, getting the good ending requires that Kei dig further into the history of the manor, and learn more about Kaname. While doing so, he discovers the other half of the earring set -- the one Rei discovers that allows her to confront and finally defeat Reika. So instead of simply killing him, Reika does exactly what Kirie did in the first game -- she keeps the splitting image of her lover with her, trapping him inside the Manor of Sleep.

And therein lies the heart of this theory. The good ending comes from getting the entire story, from fully investigating the manor and reuniting the two halves of the earring set. It is unlike any of the other games, where a good ending can be obtained simply through playing on a different difficulty setting.