Why is Cervantes' Don Quixote considered heroic if all he is doing is "tilting at windmills?"
How we view Don Quixote depends a great deal on our attitude toward ideals. Many realists, for example, as the name implies, believe that ideals are interesting but largely not relevant to living because ideals, by their nature, will always be overpowered by real life. On the other hand, there are idealists in this world who absolutely believe that taking action based on one's ideals can improve the world. We only have to look at the recent "Occupy Wall Street" and related protests to see some degree of idealistic behavior in practice.
In Don Quixote, one one level, we are presented with a old man, a relatively low-level aristocrat, whose imagination is so captured by the ideals of chivalry and honor that he turns himself into a 14thC. knight-errant, complete with squire (Sancho Panza), and journeys forth to right as many wrongs that he can. Even before he takes on the persona of a knight, we know that he kept "a lance in the lance-rack, an old buckler (to affix a sword to his side), a lean hack (his mighty steed, past it's prime), and a grey-hound for coursing." Don Quixote is already drawn to the days of chivalry because he already has a typical knight's accouterments, including a hunting dog.
That Don Quixote has completely adopted the ideals of chivalry and the plan to execute those ideals we see in the following lines:
. . . setting what wrongs he intended to right, grievances to redress, injustices to repair, abuses to remove, and duties to discharge
As the knight sallies forth to do battle with the world's injustices, Cervantes reminds us that Don Quixote really has no experience with knightly things--every bit of knowledge he has acquired about being a knight and the concept of chivalry has come to him through books, which, of course, do not depict the reality of a knight's life in the Middle Ages, but the ideal picture of knightly behavior. Don Quixote is about to take his ideal view of knighthood into the real world, and the ultimate result, of course, will be disillusionment.
During his knight-errantry, Don Quixote acquires his loyal but realistic squire, Sancho Panzo, who clearly sees that his master is deluded but admires his consistent craziness, and when the knight finds his damsel in distress, he doesn't perceive her as a sturdy peasant girl but his high-born ideal of a medieval woman. At this point, Don Quixote has all the elements of a chivalric life.
Even though, on a realistic level, everything Don Quixote does throughout the novel is laughable--tilting against windmills, addressing flocks of sheep as if they were troops--on another level we have to admire his willingness and bravery when he "risks" his life to do battle with inanimate objects--he puts his ideals into practice, which, even if we laugh, we have to admire.
The answer to the question, then, depends upon one's view of what the world is made of. If the world is made up of only the "real," then ideals and imagination may have no place; on the other hand, if one perceives the world as being better off for having idealistic people, if wrong-headed in practice, then one can look with amusement and some degree of hope on Don Quixote.
At the end, when Don Quixote is dying, acknowledges his folly, and loses his idealistic vision, the question becomes this: Was he better off with his mistaken ideals or his clear understanding of reality?