The writings of Shakespeare are often suffered through by students in literature classes, and this suffering is generally paired with one inescapable lesson: William Shakespeare is the most exalted poet to have written in English. Ever.
Shakespeare is credited with creating (either through the addition of prefixes or suffixes or through plain old inventiveness) about 1700 words that linger in today's lexicon, including the following: addiction, blushing, eyeball, lonely, obscene, swagger, and my personal favorite, madcap. To have invented one or two or even ten words that remain in common use hundreds of years after your death would be a pretty impressive feat, but to come up with well over a thousand? Well, that's just (to use one of Shakespeare's words) zany.
Be that as it may, literature students still suffer. Shakespeare's writing (along with other things, like the translation of the King James Bible) may have ushered in modern English, but to today's readers, it doesn't seem very, well,modern.
Shakespeare is popular today because any story or plot line, character relationship, theme, love, loss, death, or suicide can be traced back to one of Shakespeare's famous plays/poems. His mastering of a tragedy a comedy or an epic love story seeps into modern day literature and film making alike.