Just watch reruns of The Beverly Hillbillies. Old-timer, backwoods people from rural (country) America used to say "et" instead of ate.
"Musta been sumthin' he et."
Well, that's the way I say it, and so do all my family (who are mainly teachers) I thought it was pretty normal - but maybe it died out overseas!
Differences in spoken language can be fascinating, but are usually quite small. Differences in vocabulary are noticeable. One interesting point is that train and motoring technology developed after we'd split up - so we tend to use different terms ("ties" instead of "sleepers", "switches" instead of "points", "engineer" instead of "engine driver"; also "trunk" instead of "boot", "hood" instead of "bonnet", "gasolene" instead of "petrol". A similar point applies to "elevators" instead of "lifts" in buildings.
You also see differences in written usage on the internet. Most American publications tend to use singular verbs with collective nouns - e.g. "The Band Perry is successful", where most English people would write "The Band Perry are successful".
Past tenses of verbs can also differ slightly. Many Americans write "dreamed", "learned" and "spelled", whereas many English (including myself) tend to write "dreamt", "learnt" and "spelt". Both spellings are optional though - as are the "ise", "ize" endings of many verbs like "authorize". The "ize" endings are recommended by the Oxford dictionary, and I tend to use them - but many English people see them as old-fashioned or foreign, and prefer to write "ise" (though that's not how they pronounce them