Although Hamlet disappoints loved ones, tells lies and even murders, we are still able to sympathize with him. Why does the reader feel for him?
The character of Hamlet, though he is a prince, strikes a universal chord with readers of the play everywhere. Though the events in Denmark are specifically tied to one time and place, Hamlet's emotions, thoughts, and interior struggles transcend time and place. A great example of how this works is in the film version of Hamlet starring Ethan Hawke. It is set in the present day, at the Elsinore Corporation rather than Elsinore Castle, but Hamlet's problems still make sense in this new setting. His struggles with depression, thoughts of suicide, and indecision are timeless.
It is common to sympathize with Hamlet because of how well Shakespeare evokes internal states. However, I would argue that all the excellence in the world in this area wouldn't matter if it weren't for the external circumstances. That is to say, like a great thriller writer, Shakespeare gives us extremes, even "What if…?" situations. What if your father was murdered? What if his ghost came back from the dead? What if your uncle had killed him? And your mother married him? Ow, ow, ow!
I think that the reader has sympathy for Hamlet because he is so full of contradictions. He really gives the reader a full view of the human psyche in grief. He is a fascinating individual who explores, in great depth, the deep passions that we feel for those we love, the level of anger that can consume us and the confusion that overcomes us in challenging times of change.
Hamlet, I think draws us in because he feels everything so deeply.