In addition to the answers above, you might be interested in this thread:
Hi, not discouraging other replies, but while you're waiting, you might want to check out a couple of earlier answers:
/u/bayoris walks us backwards through time in How far back in time could you go, before modern English becomes unintelligible to inhabitants of the British Isles?
/u/cdesmoulins gives an overview & provides lots o' links to more in Could a modern english speak with a person from the medieval in england?
Follow up question: Did other languages like German have the same "evolution" that English had?
Actually, perhaps only as late as the 1600s or 1700s. From the 1300s to 1700s something called the "Great Vowel Shift" occurred which dramatically changed English pronunciation. Before the shift, the sentence "I might go and buy some meat" would have sounded more like "I meat goo and buoy some mitt".
For an example of an accent sort of "frozen in time" since the late 1600s, watch this http://www.youtube.com/watch?v=AIZgw09CG9E fairly incredible video. It's hypothesized that this accent is fairly close to what American and many British accents sounded like around 1700 (and in truth the "standard British" or "BBC" accent has changed far more since then, dropping the "r" etc (non-Rhoticizing), and many aspects American accents have stayed **relatively ** constant, though take that term with a large grain of salt).
If you leave accent aside, and are really wondering more about grammar and vocabulary, the the farthest back you could go would probably be the 1300s. Before 1066 the English spoke Old English, which looks a lot more like modern Norwegian or Dutch than modern English (e.g. "and on thaere hwile heo dreag tha losinga.." - "and in that moment she felt the loss..." - on a purely superficial level you might be able to pick out a word or two but only like in this case if you're presented with the overall meaning (e.g. you can see that common words like "and" and "hwile - while (moment)" stayed fairly constant but overall it's incomprehensible.
Here's an awesome video http://www.youtube.com/watch?v=OeC1yAaWG34 of using Old English to communicate with a modern Frisian. In 1066 the French-Speaking Normans invaded England, and for about two hundred years the country was divided - the royalty, priests, nobles, and state bureaucracy spoke a form of French, while most people spoke more like the Old English above. The two eventually merged into Middle English - the language of Chaucer: "Twenty thousand freres on a route, And thurghout helle swarmed al aboute, And comen agayn as faste as they may gon...". You can certainly get the general idea from reading it, but as the first video above demonstrates even as late as 1600s it would be difficult to understand.
There has actually been some interesting work recently in reconstructing the original pronunciation of Shakespeare (who lived ~1600), and it's very different than what you might expect: https://www.youtube.com/watch?v=gPlpphT7n9s
I would really like to know the answer to this for Danish, too. Perhaps somebody in this thread knows where to look?