Earliest : 1066 or perhaps 1054, both mentioned above.
Latest : 2030 ? Anything after date is too far away for me to really see it as a date, although 2525 is a fun example.
Lowest: 1054, the year of the Crab Supernova.
Highest: 3001, from the Clarke story.
Time was, I did not expect to live to see the century turn over. I very seldom write checks, but when I do, I have to cross out the ‘19’ pre-printed in the date field.
I recall seeing matching tombstones with a ‘19’ pre-carved … and with the surviving spouse outliving his die-by date. :smack:
The only pre-1066 date I’ve memorized is Charlemagne’s coronation in 800 — a round number easy to remember. I’ve wondered if the off-by-four error in Anno Domini was due to Charlemagne’s insistence on a round number for his coronation year! 
When I see “44” my brain adds “BC” to get the year Julius Caesar was assassinated.
When I see “753”, I automatically parse it as the (mythological) year of Rome’s founding (BCE, that is). I can’t think of any upper maximum, although anything of the form 20xx I’d recognize as a year.
Probably 1492. Probably nothing past the 21st century would I “instantly” associate as a year.
1066 Battle of Hastings was so drilled into me growing up, that I can’t see anything else when I see those numbers. (Not quite true–I lived somewhere for a couple of years where my postal code was 1066, so it did displace some of the Hastings associations over time.) I can’t think of any numbers before that with such a strong association. Highest is much tougher. The 2525 mentioned before works for me. Maybe 3001 from the Arthur C. Clarke series.
There are plenty of dates prior to 1066 that I know. But if I saw 800 written on a page, my first thought would be of it as a number rather than as a year.
Think of it as Jeopardy. If the screen shows 800, my question will be “What is two times four hundred?” not “What year was Charlemagne coronated?” But if the screen shows 1066, my question will be “What year did the Normans invade England?” not “What it two times five hundred and thirty-three?”
-4004
10,191
10,191 was the year the Atreides moved to Arrakis. Have no idea if it correlates with Earth years, however.