Next door. My mom had bought the house next door to her parents house (we used to live one block away) and a couple years later after Grandma died I moved in with Gramps.
in a two year period I moved three times within the same apartment complex. I moved from a one bedroom to a two bedroom and then later into a three bedroom. The move from the two bedroom to the three was in the same building
At once point in my university years, I moved from one residence to another across campus which was staying open for summer term. About 1 kilometer away. I think that’s it for semi-long-term homes.
My wife and I own a house that is a mile and a half down the road from my last college apartment.
But could you hand stuff from the window of one apartment to the window of the other. If not, I still have you beat (post 44). 
Right after I graduated college, I house-sat for a friend of mine who went overseas for a year. 309 West A Street, Joplin, Missouri. When he and his wife came home, I moved. To 303 West A Street, Joplin, Missouri. A distance of ~50 feet.
When my then-gf started living with me, we found a bigger apartment that happened to be about three blocks from my previous apartment.
From the second floor of a two family house to the first floor. Didn’t even have to change the address!
We moved from our 5th floor apartment to the apartment above us on the 6th floor, so 9 feet?
I moved from 2042 Argyle Street to 2128 Argyle Street so a little less than a block. That was the second shortest. In 1988 I moved from the third floor of a house to the apartment building straight across the street.
Over the course of 25 years, I lived in three different units in the same condo development, each less than 600 feet (as the crow flies) from each other, according to Google Earth. Before that I lived in two apartments that were about the same distance apart.
Same here. Place had the only pool on the block. The neighborhood girls would come over to swim in their bikinis. It was a rough life.
It’s hard to answer this because my definition of “home” is somewhat nebulous… I work long term assignments in different places for my company. When it’s time to “go home” after work, it could be a hotel, but it’s usually a rented house or apartment. Certainly I plan to leave all of them at some point and return to my hometown, but they are long assignments, usually a year to a year and a half. Or now, I’m coming up on four years, and will have been here at least five. I don’t plan to stay forever, though.
The shortest distance, I suppose then, is about two meters, but five floors down when I changed from one apartment to another when living in Interlomas, Mexico. The new apartment would have been just across the hall if it were on the same floor.
My family moved to the next-door house once, when I was a child.
Separate, non-connected buildings; the only thing they shared was a driveway.
If college dorms count, then…
- I moved from the 2nd floor (freshman year) to the 3rd floor (sophomore year) in the same hall.
- For my junior year, I moved from one dorm complex to another (about 1/10th of a mile)
- For my senior year, I stayed in that second dorm, and moved across the hallway (distance of about 8 feet).
If college dorms don’t count, then the shortest distance is between the two apartments I lived in during graduate school: 3.7 miles.
about 40 metres. When I first moved to the town I live in now I was renting on street A, then bought a house across town, but later moved to a different bought house back on street A
As a kid I lived in a house in a rural town. We moved to a new house app 2km away, but then the original house I’d lived in was relocated by semi-trailer to land literally across the road from our new place.
So, the shortest distance was a road-width, approximately 10 metres!
Does this count? 
I moved to the house across the street and one over, so about 100 feet maybe. Now this was in Isla Vista, which is less than a mile square. I lived in 4 different houses, all of which were within 2 blocks of each other.
13.2 miles. When I returned from living in Germany for 3 years, I moved to one suburb of Columbus on the east side. A year later, I moved to another suburb on the east side, where I still live. All my other moves were more than 450 miles.
This is discounting my moves in college, where I had two different apartments, plus two dorms. The shortest distance there was between my dorm freshman year and sophomore year, which was about 500 feet. If dorms don’t count, but we’re still counting college, I moved from one apartment to another in Ithaca, 3.9 miles away.
Hubs moved from a small one-bedroom to a large one-bedroom when we got married. The move was upstairs and down the hall. We didn’t bother packing much of anything, just carried stuff from one apartment to the other.
Our most recent move was about four miles from the rental house to our current house.
I dislike short moves.