All the way back to its inception. You can read the Constitution and Declaration of Independence, right? You may have some trouble with certain idioms or words, but it's nothing you couldn't pick up easily. Take a look at some of Benjamin Franklin's writings to prove it to yourself: http://franklinpapers.org/franklin//agree;jsessionid=33674AAC7495354FF1EFA017CD2B6248

Also, consider the fact that even 16th century English such as Shakespeare is easily understandable.

hi! /u/mrhet has addressed the US; you may be interested in more info in the FAQ

How far back could I go and still communicate?

and a few specific questions

I've been dropped into a town in the Old West in the 1870's. Trying to figure out what happened, I try to strike up conversation with a local miner, and then the mayor of the town. How well would I be able to understand them both?

Would Americans at the time of the revolution have spoken with a distinct non-British accent?