The significance of the title is in the futility of planning and the inevitablility of failure if the odds are stacked against you - as they are for George and Lennie. The novel is a condemnation of the American Dream, as has been said before but it also reflects on some of the principles of the American Constitution. All men are not created equal in the eyes of humanity, and characters like Lennie and George will always be judged by his weaknesses rather than his strengths.
The title is from the Robert Burns poem, "To A Mouse, On Turning Up Her Nest." The speaker observes a mouse whose carefully laid home is upturned by the cruel winter winds and bitter cold. Despite all of the mouse's hard work, her efforts are for naught: "The best-laid schemes o' mice an 'men / Gang aft agley," the poet writes (ie, often go awry.)
Likewise, Lennie and George's plans for a life of ease an "livin' off the fatta the lan'" also are forever disrupted by Lennie's accidental murder of Curley's wife. Like the mouse, neither could have foreseen the drastic turn their lives would take, despite their plans for the future.
Yes, y2kfain is right in making an explicit link between mice and men. Both in the play are shown to be immensely fragile and breakable. Lennie with his mice unfortunately foreshadows the failure at the centre of the play. Just as Lennie wants to pet the mice and keep them as pets, he accidentally and non-intentionally kills them. In the same way, George and Lennie desperately try to achieve their dream of "living of the fatta the land", but, despite their efforts, it ends in tragedy. In such a world our plans often come to naught.
The "Men" in the title of OF MICE and MEN refer to the common men who work on the ranch. For example, Slim, Candy, etc have simple desires and they are laborers. They want to obtain their own land so that they may work for themselves and obtain independence. The "Mice" in the title are an example of symbolism. Lennie loves mice, yet he pets them too hard and then they die. His fate in the book mirrors the fate of the mice he takes care of then kills accidently. Similiarly, George takes care of Lennie, yet he has to kill him intentionally. Both mice and men are fragile in regards to nature and the cruelties of humanity.
The title Of Mice and Men is in reference to Robert Burns' poem. The full phrase is "the best laid plans of mice and men often go awry." I would look at the literal meaning of this quotation and apply it to the novel as a whole.