Perhaps what makes Hamlet so relevant, giving it its meaning and significance, over time is Shakespeare's ability to portray Hamlet as such a "human" character. He is a hero in the sense that he is a great man—honest, family-centered, loving, God-fearing, and a man of integrity; he is well-loved by the people; and he is tragic in that his demise is his own fault (based on Aristotle's definition of a tragic hero).
Most people can relate to some aspect of Hamlet's admirable qualities—and his shortcomings. Hamlet loved his father: it is easy to understand how devastated he is to not only learn that his father was murdered, but that Old Hamlet's brother, Claudius, is to blame.
...Now, Hamlet, hear.
'tis given out that, sleeping in mine orchard,
A serpent stung me. So the whole ear of Denmark
Is by a forged process of my death
Rankly abused. But know, thou noble youth,
The serpent that did sting thy father's life
Now wears his crown.(I.v.39-45)
Hamlet promises to avenge Old Hamlet's death.
Ay, thou poor ghost, while memory holds a seat
In this distracted globe. Remember thee?
And thy commandment all alone shall live
Within the book and volume of my brain,
Unmix'd with baser matter. Yes, by heaven! (107-109)
Committed to seeking revenge for his father's murder, Hamlet has shortcomings with which we can all identify: is it the right thing to do (for to kill a king without true reason is a mortal sin)? Is it the best time to act? Hamlet struggles, trying to make certain he has proof enough to take the King's life. Even with proof, however, he hesitates, and Claudius eventually kills almost everyone left alive of note in Elsinore.
Hamlet turns his back on Ophelia for the sake of avenging Old Hamlet's death. He lacks faith in her: had he been more trusting, he would not have been so isolated in his quest, and Ophelia would most likely have lived, and Hamlet as well. We see his feelings clearly at Ophelia's funeral:
I loved Ophelia. Forty thousand brothers
Could not, with all their quantity of love,
Make up my sum. (V.i.270-272)
Hamlet also takes issue with his mother.
Eyes without feeling, feeling without sight,
Ears without hands or eyes, smelling sans all,
Or but a sickly part of one true sense
Could not so mope.
O shame! where is thy blush? (III.iv.84-88)
As Hamlet paints this harsh portrait of Gertrude and how she has so easily left the memories of a noble husband behind in order to consort with a man as base as Claudius, Hamlet's mother's eyes are turned within, and she see her situation clearly for the first time since the play began. She also learns that Claudius murdered her first husband, and she is shattered:
O, speak to me no more!
These words like daggers enter in mine ears.
No more, sweet Hamlet! (103-105)
Though they argue, Hamlet and Gertrude overcome the obstacles that have separated the mother and son. Their reconciliation seems to promise better times for the woman and young man who have lost a husband and father. However, this is not to be.
Hamlet speaks throughout a multitude of generations because Hamlet makes mistakes as we do. He argues with his parents, makes mistakes with the woman he loves and procrastinates until his problems become insurmountable. He is a man of love; but he also has sorrows and regrets. For even in his nobility, many things happen which are out of his control. Hamlet is very much like we are—his character is timeless.