George and Lennie actually have very little in common other than their experiences and background. Lennie's emotional and mental limitations also limit the kind of relationship the two characters can have with each other.
For one, they are both farmhands, migrant workers who go from ranch to ranch and work jobs such as "buckin' barley". In this way, they are both fairly simple, without a lot of ambition.
Another thing they have in common is their own shared history. They don't know the rest of the ranch hands, they only know each other, and the things they have been through since Lennie's Aunt Clara died.
Third, they are both generally good people, Lennie because he knows no differently, George because he's been raised that way.
Fourth, they seem to need each other, that is, they are the only real family each other has, and so they protect each other, Lennie needs George to look after him, and George needs to look after Lennie.
Lastly, they share a dream, a little place where they can "live off the fat of the land", and no one could "can" them. Lennie, of course, gets to "tend dem rabbits".