This is sort of an off-the-wall suggestion, but I thought I'd put it here and see what people thought.
The basic premise is that brewing an emerald into an awkward potion would produce a potion of peace. When splashed on mobs, it would make them non-hostile for 30 seconds, though they would still become hostile if you attacked them (up to 60 seconds with redstone added, and with the added bonus of them not becoming hostile when you attack them when you add glowstone).
Brewing into this potion a fermented spider eye would make a potion of hostility. This potion would cause mobs to be hostile to the nearest mob or player for 30 seconds (though they would still shift their attentions to the last mob or player to attack them). Redstone extends this to 60 seconds, and glowstone causes mobs to move to the next nearest mob once they kill their first target.
Now, why an emerald? Two reasons. Firstly, emerald is sufficiently rare. Secondly, the emerald is what you trade with villagers. It represents the peaceful interaction you have with the villagers.
In what situations might something like this be useful? When dealing with large amounts of mobs, or when you are out at night, but just don't want to fight. Why wouldn't you want to fight? If you are traveling, you want to conserve as much time as possible. My previous suggestion (potion of fullness), allows you to conserve precious eating time. This allows you to travel at night without having to stop to fight, not only conserving time, but actually increasing travel time because you don't need to stop at night to dig a shelter and sleep. Another use is if you are working with mobs, such as in a mob system, or if you are studying behavior and pathfinding.