In Of Mice and Men, Lennie and George dream about owning their own farm and living off of the land.

The American dream is the belief that everyone has an equal opportunity for success, provided that they work hard. Of Mice and Men is set during the era of the Great Depression when, despite extreme shortages, people still clung to the idea of the American dream. Ultimately, what Steinbeck demonstrates with Lennie’s death is that for some people, despite determination and drive, the American dream is unattainable and can even be somewhat of a trap. However, Lennie and George's dream is what keeps them together (see quote below) and striving for something greater. So, although the American dream is just a fantasy, perhaps it is necessary for living a fulfilling life.

Guys like us, that work on ranches, are the loneliest guys in the world. They got no family. They don't belong no place....With us it ain't like that. We got a future.... An' why? Because...because I got you to look after me, and you got me to look after you, and that's why.

Another event illustrating the futility of the American dream is Curley’s wife’s death. She revealed that her dream was to be a movie star, but she is unable to escape her unhappy marriage and life on the ranch. Her dream was unlikely to ever materialize, but Steinbeck absolutely crushes even the possibility by penning her death at the hands of Lennie.

Crooks also allows himself to become carried away with the thought of hoeing the garden on George and Lennie’s future farm, but the underlying sense is that this will never happen. Moreover, Crooks himself explicitly says that American dreams are impossible:

I seen hunderds of men come by on the road an’ on the ranches, with their bindles on their back an’ that same damn thing in their heads. Hunderds of them. They come, an’ they quit an’ go on; an’ every damn one of ‘em’s got a little piece of land in his head/ An’ never a God damn one of ‘em ever gets it. Just like heaven. Ever’body wants a little piece of lan’. I read plenty of books out here. Nobody never gets to heaven, and nobody gets no land. It’s just in their head. They’re all the time talkin’ about it, but it’s jus’ in their head.

Steinbeck conveys the message that the American Dream—which can be defined in the context of this book as people's ability to control their own land and destiny—is not available to the American working person. Steinbeck conveys this message about the inaccessibility of the American Dream through the fate of his main characters, Lennie and George. They dream of owning their own farm where they can raise crops and rabbits and are not subject to the management of cruel farm owners. This dream is not realized, though, because George mistakenly kills a woman, so Lennie must kill him to avoid the authorities further inflicting damage on George. Candy, an elderly farm worker, symbolizes the working man's inability to achieve the American Dream. He becomes entranced by the dream Lennie and George have of owning their own farm, but he also fails to achieve this dream. It is clear that the farmhands in the book will meet tragic ends in which they either die or face lives of unending work with little to show for it.

How does Steinbeck explore the theme of dreams in Of Mice and Men?

The title, Of Mice and Men, comes from a Robert Burns poem "To a Mouse." One of the lines is "The best laid schemes o' mice an' men / gang aft agely." (The best laid plans of mice and men often go awry). 

George and Lennie's plans (dreams) of the farm often go awry because Lennie's lack of social skills often leads to bad situations; sometimes someone gets hurt (or killed). Of course, this is unintentional but it is still a constant reality they must deal with. The larger reason their dreams are never realized is because they are itinerant workers. It is difficult for them to stay on a job for a substantial amount of time because of the nature of the job, but also because Lennie always gets into trouble. 

Also, their dream has become so idealized that, even if they were ever to get a farm, it would never live up to their expectations. 

One of Steinbeck's comments on dreams is that they are idealized or romanticized. In addition, the reality for Lennie and George is that their social position (being laborers with little education) does not give them much opportunity to pursue those dreams. Lennie's social awkwardness aside, migrant ranchers had a harsh life and upward mobility was not a guarantee no matter how hard one worked. 

Crooks knows firsthand the social and economic obstacles in pursuing such idealized dreams. In Chapter Four, he tells Lennie what he thinks is the brutal reality or ranch life. 

"I seen hunderds of men come by on the road an' on the ranches, with their bindles on their back an' that same damn thing in their heads. Hunderds of them. They come, an' they quit an' go on; an' every damn one of 'em's got a little piece of land in his head. An' never a God damn one of 'em ever gets it. Just like heaven. 

The best laid plans go awry. This isn't because Lennie, George, or Crooks are not worthy or determined enough to achieve their dreams. There are external social forces (and internal if you count Lennie's mental handicap) that make it difficult if not impossible. 

In Of Mice and Men, what message does John Steinbeck offer about dreams and goals?

Steinbeck's message about dreams in Of Mice and Men represents the general theme of American Modern Literature--disillusionment (especially with the unreachable American Dream). Almost all of the characters in the novella demonstrate this theme of unreachable dreams/goals. Here are some specific examples:

1. George and Lennie--The main companions simply want a place of their own where they don't have to worry about people driving them away or bossing them around.  They want to leave loneliness and shiftlessness behind and have a permanent place.  Of course, not a single part of this dream comes true for George and Lennie.  They come so close to obtaining the farm, but all is lost when George must kill Lennie to prevent Curley from getting to him.  George is left alone and hopeless.

2. Candy--Candy simply wants to be needed and useful. He jumps at the opportunity to go in on the farm dream with George and Lennie, but all that is lost when Lennie kills Curley's Wife.  He, too, is left without his farm, without a friend, and without even a dog.

3. Curley's Wife--Curley's Wife dreams of attention and praise.  She wants to be a movie star but marries Curley instead.  She is stuck in a loveless, abusive marriage with no way out.  She dies never realizing her dream.

4. Crooks--Crooks wants equality and companionship.  He first agrees to go in on the farm dream with Candy, George and Lennie, but then backs out when Curley's Wife threatens him with false accusations. At the novella's end, he is left with his isolation and books.

Steinbeck's own disillusionment with dreams and goals is understandable especially since he concerned himself with the plight of Okies and migrant workers during the Great Depression.  His message is not unlike Fitzgerald's portrayal of unreachable or corrupted dreams in The Great Gatsby.