How would you characterize the relationships of the pairs in Of Mice and Men: George and Lennie, Candy and his dog, and Curley and his wife? ...

These relationships are all co-dependent to a certain extent.  That means that both parties to the relationship need each other.

George and Lennie travel together.  Lennie needs George, because he has developmental delays.  George also needs Lennie, though, because he likes the company and he likes having someone to work with. 

"Sure," said George. "We kinda look after each other." He indicated Lennie with his thumb. "He ain't bright. Hell of a good worker, though. Hell of a nice fella, but he ain't bright. I've knew him for a long time." (Ch. 2) 

George and Lennie traveling together is pretty unusual for migrant farm workers.  Slim is impressed by their dedication to one another.  George looks after Lennie and protects him from himself, since Lennie has no impulse control and would not be able to keep a job without him.  George likes telling Lennie about his dream of owning land someday. 

Just as George relies on Lennie for company, Candy relies on his dog.  The dog is old, and smells.  Most of the men want him to put it out of its misery.  Candy loves the old dog though, and can’t bear to see it go. 

The old man squirmed uncomfortably. "Well- hell! I had him so long. Had him since he was a pup. I herded sheep with him." He said proudly, "You wouldn't think it to look at him now, but he was the best damn sheep dog I ever seen." (Ch. 3) 

The men tell Candy he can just replace his dog with another dog, but that would not be the same for him.  Candy’s dog depends on him to take care of it.  Another dog just would not be the same.  The dog is his companion. 

Finally, Curley and his wife have a strangely co-dependent relationship because she is extremely lonely and has no one but him to talk to, and he needs her because he is terribly jealous. 

“… Ever' time the guys is around she shows up. She's lookin' for Curley, or she thought she lef' somethin' layin' around and she's lookin' for it. Seems like she can't keep away from guys. An' Curley's pants is just crawlin' with ants, but they ain't nothing come of it yet." (Ch. 3) 

Curley is always afraid that something is going to happen between his wife and one of the other guys.  She, on the other hand, is considered trouble.  The guys do not mess with her, because they do not want to mess with Curley.  Throughout the book, she is always looking for him and he is always looking for her.