Because your professors make you? :-)
Just kidding. I think we still read Shakespeare today for a variety of reasons, but here are my favorite two. First of all, Shakespeare's characters are still recognizable in the modern world, in a way that few other characters of the era are. Romeo and Juliet endure because we see our love-sick teenage selves in their adoration for each other (even if we don't commit suicide over the relationship). Bottom, the original Will Ferrell-esque buffoon, can still make us laugh with his false egotism. And we fear becoming Lear, a man addled with old age and grappling with the loss of his youth.
Secondly, we continue to read Shakespeare for the sheer beauty of his language. Yes, sometimes it's difficult and takes a long time. But taking time to peel away the layers of wordplay and multiple meanings reveals great treasures. Plus, he was so careful to craft his language in such a way that each line is music. And that music is unique to the character. If you listen to (read) them carefully, each character has a unique voice that reflects his or her personality, background, and value system.
Best of luck with your paper.
Generally, Shakespeare is still read today for a few reasons: the beautiful poetry, the multi-dimensional characters, and intricate, interwoven plots. His plays contain universal themes that still resonate today.
In the case of "Othello," those themes include jealousy, love, and racial intolerance. As long as people continue to fall in love (or at least in love with the idea of love), people will be jealous. We can learn much from Othello's mishandling of his marriage as well as through watching his manipulation by Iago. In terms of racial intolerance, while we have come far (witness the election of an African-American to our highest office), there is still work to be done in our understanding and acceptance of people who are different.
Actually it is not the racial aspect of othello that was meant in the title character. However with the changing times that is what our culture has come to believe. It was actually moor as in arabic that Shakespeare was getting at, that is why they refer to othello's witchcraft in capturing the heart of Desdemona, it had nothing to do with his race, but his religion that made him an opposing character in the play.