What keeps Lennie and George together, considering their complex relationship, the difficulties they face, and their differences from others they encounter?

There are a number of things that keep the two men together. First, they seem to have a deep affection for one another. Even though they sometimes squabble, it is obvious that they care about each other. George, for example, apologizes to Lennie after having scolded him harshly in chapter one, as the following extract indicates:

George looked quickly and searchingly at him. "I been mean, ain't I?"
"No--look! I was jus' foolin', Lennie. 'Cause I want you to stay with me. Trouble with mice is you always kill 'em." He paused. "Tell you what I'll do, Lennie. First chance I get I'll give you a pup. Maybe you wouldn't kill it. That'd be better than mice. And you could pet it harder."

For his part, Lennie sees an advantage and knows he can manipulate George, threatening to leave him. The two men make up, however, and George, at Lennie's urging, starts talking about how different they are, as migrant workers, to other men in their situation.
The two men's dependence on each other also keeps them together. When they speak about what makes them unique, they often relate how they are there for each other. Unlike other men, they have each other to turn to, as George states when he refers to the loneliness other ranch hands experience:

"With us it ain't like that. We got a future. We got somebody to talk to that gives a damn about us. We don't have to sit in no bar room blowin' in our jack jus' because we got no place else to go. If them other guys gets in jail they can rot for all anybody gives a damn. But not us."

In addition, as George has mentioned, they "got a future." He is referring to their plan to buy a ten-acre piece of land and run it on their own. They are working to put together a stake. Their dream is to gain independence and determine their own destiny. They would be able to freely exercise their choice about whom they want to associate with and how they wish to spend their time, unlike other workers who will always be dependent on someone else. Those men will never be as independent as they plan to be. Such men will always rely on someone else, such as a ranch owner, for an income, while George and Lennie will be self-sufficient. Both George and Lennie are enthralled by the enormity of their dream, for it is what makes them special and is a primary factor in what keeps them together.
Furthermore, although George consistently complains about Lennie limiting his freedom, he enjoys the companionship his friend provides. He has someone to talk to and with whom he can share his feelings and frustrations, someone he can confide in. This also makes them different from the others, who have no one to trust or confide in.
It is tragic that their dream in the end comes to nothing when Lennie, unfortunately and unintentionally, kills Curley's wife and has to flee. George follows him and kills his companion in an act of mercy.