So even though the "other" might be aliens or faery folk, the "other" can be our fellow humans. People who live right next door to us.
...truthfully, when I sit down to write this post I was not going to start out by talking about the "other." But it occurred to me that it is totally relevant to my subject, so I figured I may as well start out with it.
What I do want to talk about is that some stories are concerned with relationships that bridge the gap that separates people. Since we're using the phrase "the other" to describe those who are totally separate, let's use the phrase "the same" to describe the people in the stories I'm thinking of.
Novels in which you have two characters who are "the same":
Inheritance Cycle by Christopher Paolini
Think about the dragons and their riders. The two are very close, and are in each others heads all the time. In fact, they can get so in each other's heads at times that they think and act as one, and are basically one person with two bodies. If one dies, the shock usually kills the other.
Pern books by Anne McCaffrey
Again, dragons and their riders share a special bond. And like in Paolini's books, the shock of one dying usually kills the other.
Twilight books by Stephenie Meyer
I'm thinking of the werewolves. When they're in werewolf form, they hear each others thoughts. (I'm not counting Edward Cullen's mind reading here because that's a one way thing, and I'm talking about two way relationships.)
Green Rider series by Kristen Britain
They aren't in each other's heads, but there is a special bond between the green riders and their horses. If one is killed, the other is devastated. In one case a green rider and her horse are separated by a great distance, but because of the bond the horse manages to find its rider despite the great distance.
Joust series by Mercedes Lackey
There's a special bond between the dragon riders and their dragons. The dragons aren't as intelligent as in McCAffrey's and Paolini's books, nor are the dragons and riders in each other's heads. But like in Britain's books, if one is killed the other is devastated.
Valdemar series by Mercedes Lackey
Another case of a human and horse. Except that the horses aren't horses, they're something else that are just as intelligent as humans. In the one book I read, the boy can talk mind to mind to his horse, even if they aren't right next to each other.
Dragonlord books by Joanne Bertin
Each dragonlord has a soul twin (I think they're called soul twins). No dragonlord is a complete person without their soul twins. Also, each dragonlord has a horse to ride when they travel in human form, and I seem to recall that there is a special bond between the dragonlords and their horses.
There is always an "other" in each of the novels listed above, but my point is that there's also a relationship that is the complete opposite of the "other." That is, there's always a relationship that exceeds that of what normal humans are capable of, unless we somehow find a way to get in each other's heads. In these relationships I call the two individuals the "same."
...and I notice that in each story listed above the special bond is never between two humans, unless you count the werewolves as humans, in which case you would also count the dragonlords as human.
If anyone has another book to add to this list, please feel free to mention it in the comments.