My favorite subplot in A Link Between Worlds is so simple and subtle but so effective.
The blacksmith and his wife in Lorule. They're the first people you meet in the world (apart from Hilda) and they're... kind of jerks. The wife is the one that pulled you off the road but questions why she even bothered, acts snippy when you wake up, and wants you to immediately get out and on your way as soon as you're capable. The blacksmith is meanwhile just a grumpy guy, disinterested in anything. He even thinks your legendary Master Sword is an amateur's work! Really paints a good picture of how the populace of Lorule isn't exactly in the best spirits due to the condition of their entire world, but they still don't exactly make you sympathize with their behavior.
That is... until the blacksmith sees you with your tempered sword from Hyrule. He takes interest in your upgraded sword and considers it a fine job, though boasts that he could do better. But he's in better spirits, wanting to prove himself and asking you to bring him Master Ore to upgrade the sword even further. He's fired up, which surprises his wife. And, once your sword is upgraded, he feels much better and even thanks you for the opportunity, and his wife is reminded why she fell in love with him in the first place. Even the dwarven blacksmith is happier with the new atmosphere. Even though the world is basically doomed, you've managed to brighten up these people's lives a little.
Again, it's really subtle, but I think it's my favorite part of the game, story-wise.