1379 miles from Los Angeles to Austin.
Across the courtyard of the apartment complex, probably about two football fields (720 feet?)
Surprising how many of us moved from one apartment to another. I guess mostly it was to get more space? For me it was; from a one-bedroom upstairs to a two-story, two-bedroom with a basement and a carport. For which we paid $190 per month (95 each for me and my roomie). Ah, those were the days.
Shortest. 3/4 mile when in Uni.
Longest. Oslo - Boston this fall. 3490 miles.
Shortest was across the hall.
Longest was Columbus to LA.
Shortest is maybe a mile. I was living with my two best friends but I was starting to make a little more money and I wanted my own place. I could still walk balk to the old apartment from the new place.
Tied with that was when I said, fuck this, and moved back to that apartment.
Longest was about 3,000 miles, moving from Portland, ME to San Francisco, CA when I got married.
Tied with that was when I got divorced and moved back.
Oddly, my current house is about a hundred yards from an apartment I used to live in about twenty-five years ago. Not quite a full circle, but a weird loop around.
Longest was New Zealand to New York, 8,800 miles.
Shortest for a place I would call “home” was within the same apartment building, from the first floor to the 15th.
For temporary accommodations, I moved between three adjacent rooms in the same building when I was a student.
Shortest—from the second floor apartment of a two-family house to the first floor apartment.as with someone else our old floor became our new ceiling, more or less.
The shortest for me was across the parking lot of an apartment complex, from a two-bedroom to a three. That might have been the biggest pain in the ass move of my life, too. Most of the stuff was just carried over, which made the whole ordeal seem to last a lifetime. Minus the satisfaction of actually seeming to having a new home.
The longest was from South Carolina to Illinois. Possibly tied for biggest pain in the ass. I was following my friends in the moving truck. Friends who did not make sure I was still behind them when they stopped for gas. I had no idea, and kept going on my merry little way. I ended up taking the scenic route through an extra state or two, oblivious to the fact that I had missed changing highways. Yeah, this was before the days of navigation apps. I arrived in Illinois a day later than everyone else. 
How about moving zero feet*?
From 562 Greenwood Avenue to 833 Monroe Circle.
By remodeling and using the former side door as the front door.
The kids still say they miss the old “Greenwood Avenue house”: “The neighborhood was so much nicer!”
*That’s zero meters for you Euro-types…
(zero rods for you 15th century peasants)
Shortest: about two blocks
Longest: Kampala, Uganda to Anchorage, Alaska via MSP, about 10,000 miles.
Like Morgenstern, moving from 1-BR to 2-BR apartment, didn’t even have to change floors, just about a 100 foot walk.
Longest was from Huntsville, Al to Abu Dhabi, UAE, and four years later, back to Huntsville.
In 1985, I moved from Broomfield, Colorado, to the University of Lancaster in the UK. Google informs me that this is 4,484 miles.
When I first moved to the DC area, I had a basement apartment in Silver Spring off Georgia Ave, just inside the Beltway. After a couple of months, I moved out to share a house near the Forest Glen Metro, off Georgia Ave, just outside the Beltway. About a mile apart.
I was going to say that…
My shortest move was across the street, from a townhouse complex to an apartment, with the guy I was renting a room from. And the moving van broke down in the middle of the road between the two places. This was during second year when I was in electronics school.
My mom and I moved two doors down when I was in high school.
But you beat me.
Changing apartments in my college days is probably the shortest. All in the same city and not more than a mile or so apart.
Longest is probably Houston to Kwajalein.
Longest was boise idaho to hinesville ga
Shortest was out the back door of my parent’s house into a 20’ travel trailer i bought and parked in their backyard when i was 19
Straight-line distance:
As a child (three- and four-years old) we moved from Anaheim, CA to Haiyama, JP, a distance of about 5,500 miles.
As an adult, in 2003 I moved from L.A. to Birch Bay, WA, 1,056 miles.
Shortest: .4 miles from my childhood home to my current home
Longest: see above
Shortest: from the New Hampshire to Maine (17 miles as the crow flies).
Longest: from West Virginia to New Hampshire (585 miles ATCF).
Moved to the bedroom next door in a rental house during college when we shuffled roommates.
Longest: Chicago to Dallas
Shortest: not counting dorm room changes in colleges, slightly more than 1 km.