While Shakespeare was producing much of his work hundreds of years ago, he belongs to the Early Modern era of the English Language. This particular period started approximately 60 years before he was born.
Many of the comments seem to think that the stilted grammar and flow (that only occur to current speakers of the language)determine whether a work is written in Old English. Some have mentioned Beowulf, which very few have likely read untranslated. If you can't understand a translated work, blame the person who authored IT and not the original work.
Old English approximates a German sound. If one were to hear something read in OE, they may guess the language was an older form of German. Middle English, the sort you'll come across reading UNTRANSLATED Chaucer, is much closer to what many would recognize as an English sounding language. It was highly ornate and approximated and Irish sound.
Early Modern English is basically what we are provided with when encountering Shakespeare. The language isn't as difficult to navigate as the references, especially in Shakespeare, which are historical as well as contemporary.
When considering the importance of Shakespeare or works that came before him, it is useful to consider the endeavor as trying to find one's cultural heritage. Many of today's popular literature is founded, deeply, in what has come before us. Irreverance and often the backdrops surrounding our most beloved characters have references much older than many can imagine. Even Harry Potter closely resembles elements of Beowulf, Chaucer, and Shakespeare to name the 3 of the more recognizeable.
Literature that has come before our time does tend to get treated with a little too much reverance, but the reasons people consider these classics to be important can't be denied.
This volume, lacking footnotes and perverting line structure, is still nifty in it's economical purpose, and is worth owning if you can make use of it.