How far back in time could I travel and still be understood?

It largely depends on your current dialect. Regions of the English-speaking world vary in pronunciation to the point where communication can be impossible. For example, my Canadian-influenced Upstate New York dialect often goes with a lot of blank expressions in West Virginia. Even in Boston, I'm sometimes caught in a loop of both speakers asking to repeat each other.

So, adding time into the change of the language, it's not impossible to say that even one hundred years back in time would be immensely difficult, depending on where you go. Supposing you only needed to speak to one or few English speaking persons, and you had foresight on where to travel, you'd be in much better shape.

You'd probably be hard-pressed to understand anyone at first in Shakespearian times, though, unless you speak a rural dialect in England - the language we associate with Shakespeare is a highly Romanticized ideal of England that came out of the 19th century. In fact it's closer to what we might think of as an Irish accent (Check around minute 2 in this video for a comparison of Received vs Original English: https://www.youtube.com/watch?v=Hi-rejaoP7U)

Bear in mind that Shakespeare wrote beautifully, and everything fell into place, ultimately shaping the whole language that came after him. The commoners did not have his eloquence. Top it off with the slang of the day that never became canonized by print (there was a lot), you'd have your work cut out for you any time before, say, 1700.

Any time before the Norman Invasion, and you would be speaking an entirely foreign language.

I gather this is largely about spoken English so I will focus on that.

Long time ago, one of our teachers played us an audio version of the General Prologue to Canterbury Tales, in a reconstructed pronunciation. It was from a tape then, but similar versions are available around the net now. Here's one.

Even dipping one's nose into a facsimile of the Prologue leaves one unprepared for this, I'm afraid. The vowels and the consonants, not to mention the basis of articulation, are quite different from what we are used to today.

Canterbury Tales were written in the southern dialect (between ca. 1380 and 1400), i.e., in the dialect from which modern standard English largely evolved. Parallel to Cantebury Tales in the south, one may look at the poems of the Pearl Manuscript. Here is a transcription of Pearl, section 1 (it is admittedly alliterative, which may be occlusive; a normal chat would not be so), in the Northumbrian dialect. (Cf. the Wikipedia entry for 14th century Middle English.)

All in all, I think, one would have a great lot of trouble understanding, or makine oneself understood, around AD 1400. (With marginally better chances in the south, perhaps, unless one is akin to the northern dialects of today, language-wise.)

Even in Elizabethan England, pronunciation (of vowels especially) would take us by surprise, as the vowel shift was still taking place by then. (Again we're talking south of England.) Not to mention the vocabulary.

By way of an example, we recently had a question here at ELU on Adam lay ybounden, a 15th century English carol.

By and large, I believe up to three hundred years back would land one in a setting where one might make oneself basically understood, as to pronunciation and vocabulary.