In Of Mice and Men, there aren't many especially convincing examples of characters with dreams that positively affect their lives. Indeed, the book is set in the 1930s, when a combination of factors, such as the Great Depression, the Dust Bowl, racism, and sexism, made it very difficult, if not impossible, for people to realize their dreams. The character who gets closest, however, to having a dream which positively affects his life is Lennie.
Lennie has a dream which is his own personal interpretation of the American Dream that George aspires to, only with multicolored green, red, and blue rabbits, rather than the more traditional kind. In the story, Lennie repeatedly pleads with George to tell him about the rabbits. In chapter 1, for example, Lennie pleads, "Come on, George. Tell me. Please, George. Like you done before." George then tells Lennie about a time in the future when they will "have a little house and a couple of acres an' a cow and some pigs...a big vegetable patch and a rabbit hutch and chickens." This dream motivates both George and Lennie to keep going and keep working hard. It's also a reason for Lennie and George to stick together, which is unusual for itinerant workers at this time. If they stick together, it means that they will be able to pool their wages and purchase the land together. And sticking with George, because of this dream, undoubtedly makes Lennie's life, temporarily at least, better than it would otherwise be.
Without George, Lennie would likely find it very difficult to get work and even more difficult to keep it. It is also likely that, without George, Lennie would have been locked up, or worse, for touching the girl's red dress in Weed. It was only with George's help that Lennie managed to escape Weed and the lynching party that pursued them after the girl cried rape. In chapter 1, George also says to Lennie that, on his own, Lennie wouldn't be able to find food to eat and that "somebody'd shoot [him] for a coyote." This may be a slight exaggeration but probably isn't too far from the truth.
Therefore, Lennie's dream of owning a piece of land with George, and living "offa the fatta the lan'," positively affects his life because it means that he stays with George, who protects and helps him. This dream also makes George and Lennie's relationship stronger, because it provides them with "a future" and "somebody to talk to." George and Lennie are not like other itinerant working men, who "are the loneliest guys in the world," because, as Lennie says, "I got you to look after me, and you got me to look after you." Indeed, whenever Lennie is with George, and particularly when George is reminding Lennie of their dream, Lennie is very happy. It is difficult to imagine that he would be happy without George or without the dream that he shares with George.