If I went back in time what would be earliest that I could understand spoken English?
It depends a great deal on your “ear for dialect” – if you can understand a Scotsman or someone speaking Strine, you’ll be further ahead when your time machine stops in 1740 or 1560.
Note that “tea” used to rhyme with “stray” – we even have traditional songs which show that old pronunciation, and Alexander Pope used it in the late 1700s.
That said, you’d find Elizabethan or Jacobean English understandable if somewhat strange-sounding. Getting back much before that, say to Henry VII’s time, you might have some problems. And when you get to the early 1400s, Middle English is nearly a foreign language.
Depends…
Here is an example of Old English (c. 1000)
Fæder ure þuþe eart on heofonum
si þin nama gehalgod tobecume þin rice gewurþe þin willa on eorðan swa swa on heofonum
urne gedæghwamlican hlaf syle us to dæg
and forgyf us ure gyltas swa swa we forgyfað urum gyltendum
and ne gelæd þu us on costnunge ac alys us of yfele soþlice.
Move up to Middle English (c. 1384) and most people can sort it out.
Oure fadir þat art in heuenes halwid be þi name;
þi reume or kyngdom come to be. Be þi wille don in herþe as it is dounin heuene.
yeue to us today oure eche dayes bred.
And foryeue to us oure dettis þat is oure synnys as we foryeuen to oure dettouris þat is to men þat han synned in us.
And lede us not into temptacion but delyuere us from euyl.
By 1611, it becomes essentially modern English.
Our father which art in heauen, hallowed be thy name.
Thy kingdom come. Thy will be done in earth as it is in heauen.
Giue us this day our daily bread.
And forgiue us our debts as we forgiue our debters.
And lead us not into temptation, but deliuer us from euill. Amen.
The above is from the History of English page at Wordorigins.org
http://www.wordorigins.org/histeng.htm
I hope this helps!
John Ford used that pronunciation in “The Quiet Man,” set in rural Ireland of the early 1920’s. I can hear John Wayne now, throwing open the door and shouting “Woman of the house! Where’s me tea?” 
Funny, just this week I did a little activity in most of my higher-level English classes about how the English language has changed over the past thousand years. (I even used some of the same versions of the Lord’s Prayer just cited by daffyduck!) We also discussed how easy it would be to understand people speaking English if we travelled back to different points in time.
When I look at written Middle English I feel I can generally get a good idea of the meaning, even if I can’t understand every word. However, it would probably more difficult if I had to listen to it spoken with the pronunciation of the time. When reading I know I’m mentally adjusting things to reflect modern pronunciation, like not voicing “e” at the end of words. Were I thrust into a Middle English-speaking environment I think I’d be able to get used to the different pronunciation after a while, but it would probably be pretty difficult at first. Not as difficult as picking up a completely foreign language, but harder than understanding most modern English dialects.
But that’s all written. You forget pronunciation. Middle English is very easy to read if you do it out loud (and know what the thorn stands for). On the other hand, the English accent has changed a great deal over time, and there have been vowel shifts. Writing in 1400 can be pronounced phonetically such that it is understandable in Modern English; writing in 1611 looks like modern English already; but the person who wrote those things down would have had an entirely different idea of how they were pronounced. For a theatrical example, see this page. None of the changes are major but taken as a whole it would take some getting used to were you plunked down in the middle of a crowd who spoke like that. You’d probably get used to it, but be confused for a while.
Good search & link Astro! Thanks. 
Just be careful of comparison based on prayers-- they tend to be the most conservative parts of a language. Even in the English of today, the first line of the Lord’s prayer contains 3 archaic words (art, hallowed, thy) that most people would puzzle over were they not familiar speciifically with “Church English”.
Well I’m sure glad everyone likes to nit pick me.
How far back could you go and still understand spoken English?
It is impossible to say with any certainty. It depends.
It depends on a lot of factors. Are you a native English speaker? What part of the world were you living in when you learned English? Do you speak any Germanic languages? What level of education do you have? Have you ever read Chaucer in the original Middle English? Do you have a good ear for accents? Can you understand all speakers of modern English? Do you mean fluent immediate undertsanding or do you mean could you sort it out given a bit of time? Do you mean a prefect understanding of every single word or do you mean get the gist of things? What social class will the speakers be that you are communicating with? Will there be context clues as to what is going on?
When you ask a general question, you get a general answer. IN GENERAL, most people find that Middle English is understandable with effort. I can make sense of Chaucer, can you? If not, then Middle English is probably too far back for you. If you also speak German and Dutch and have studied Old English, then you could probably go back further than Middle English. Can you understand Shakespeare? If not, then you could probably go back about 30 minutes.
Since audio recordings didn’t exist until Edison came along, all this hoo ha about pronunciation is just conjecture. Granted it is based on a knowledge of linguistics and of the WRITINGS OF THE TIME, but it is still not a perfect science and so it is really conjecture. I’m not saying it is pure guesswork, but how well you understand the written words of the times is most likely not a bad guage of how well you might understand the spoken words of the times. Last time I checked, written language was at least nominally based on spoken language.
The OP was asking an offhand question. Give me a friggin break. I provided a link to a page that seems to me to be a rather good one page history of English. Read it and answer the question for yourself.
By the way, if you’d like to have a go at 16th century writing a bit more challenging than good old Bill, try Golidings translation of Ovid from 1567. Online here:
http://www.elizabethanauthors.com/ovid00.htm
If you’d like a bit of Chaucer in Middle English, you can find some here:
Would everyone please now get off my back? I’m old and I can barely support my own weight without you lot jumping on for fun.
A little testy today, huh?
English fixed (ie, froze) its spelling conventions considerably longer ago than many European languages. It is one of the worst examples for comparing written and spoken words over the years.
I’ve heard Chaucer read out loud and it’s **extremely ** difficult to understand. Most of the vowels were pronounced diffenetly (closer to their continental counterpars) and most of the “funky” spelling conventions we encounter today were pronounced phonetically then.
This page will illustrate the situation very well. Be sure to listen WITHOUT looking at the written version and see how well you understand the poem. Then go back and read it. I’d be surprised if you (the general “you”) would comprehend even 50% of the spoken version, whereas it’s pretty easy to get 80 - 90% of the written version.
It’s certainly reasonable to assume that the OP is asking how much someone untutored in older versions of English would understand-- saying that you’d understand Old English better if you had studied it is hardly helpful as that is true of anything.