In the best sense, Don Quixote believes the best about everyone in his life. As mentioned, a prostitute becomes a lady worth fighting for and a faithful nag becomes a fighting steed. There is, of course, a need to be realistic; however, many of us do want to see the best in others and in our circumstances. That characteristic alone makes us like Cervantes' knight-errant.
You will, no doubt, receive many answers to such a question. I think that there is a sense of Quixote in all of us to the extent that we possess and nourish the ability to dream. Quixote was such a powerful and compelling figure because he did not see things as they were presented. Rather, he saw what could be. In a world dominated by existential notions of "what is," Quixote reached back to notions of Romantic chivalry and saw a transformative vision of the what can be. He sees a windmill, and monsters need to be slew. He sees a prostitute, and his fair Dulcinea emerges. The idea of possessing an eye that transforms reality into our own subjectivity might be where there is an element of Quixote in many individuals.
The character of Don Quixote has become so famous that it is still used today to satirize politicians who have delusions of grandeur and the self-righteous who believe themselves religiously worthy and involved in great causes. For the most part, Don Quixote lives in the world of his imagination, not unlike some people on Facebook who recreate themselves and their adventures. Like Don Quixote theirs is a life of somewhat deluded grandeur.
The critic Carroll B. Johnson gives this viewpoint of Don Quixote:
Don Quixote's madness propels him backward in life. It enables him to have a life, to engage in meaningful activity, and to involve a fulfilling, revolving relationship with another human being.
That there are parallels here to some modern people is evident. Certain websites allow people to recreate themselves, to engage in activities only in cyberspace, and to connect with people with whom they could not do so otherwise. They can be envied and looked up to in cyberspace when such esteem could not be earned in real life.
I think that there are a couple of things about Don Quixote that are common to a lot of people (at least I know I see them in myself at times).
First, many of us have impossible dreams or lost causes that we try to pursue. It is really a part of being human to want things that you cannot have and to constantly try to achieve things even if you may never manage them.
Second, I think that it is not unusual for us to be mistaken about what has gone wrong in our lives. We often think that the bad things in our lives are caused by one thing when in fact they are caused by something else entirely.