Out of anywhere
When I moved out of my third home , I left behind 4 of the harry potter books by mistake
I don’t think I’ve ever left anything behind that I’d regret losing. I’ve always doublechecked everything. The things I’d hate to lose are last to go, so I can keep a closer eye on them.
When I last moved I left for last a fragile glass sculpture of two cranes, by the glass artist Mitsugi Ohno. I picked it up, and my mom opened and shut doors behind me as I left the apartment, walked down the stairs, got in and out of the car, and entered the new place. I didn’t even want to take the chance of wrapping it.
I’m proud to own anything this man made
My baseball cards when I went to college. My mom took them to the church rummage sale. Mantle and Mays rookie cards.
Nothing. I moved stuff most people would have decluttered. (I started to declutter but soon realized it would take me forever.)
I expect for most people it would be large, heavy stuff such as furniture and appliances.
Does a pool count? I had recently had the liner replaced, I had replaced the filter and pump myself pretty recently also. An in-ground pool is pretty much a hole in the ground you fill with money.
The house!
A hand sander that was a gift from my wife.
When we moved out of our rental home in suburban Philadelphia, I left behind the frame and trays of a fluorescent light plant growing stand. Cost me something to replace, but there just wasn’t room in the rented truck.
*I later learned there was a semi-frenzy in the neighborhood among people coming by to snatch up not only the plant stand, but a variety of other inexpensive oddments we left out with the garbage as well as plants and shrubs they dug up from the garden. A couple of over-enthusiasts even tried to haul off the outdoor A/C unit, which must have pleased my sleazy landlord no end. 
I once had a cherished memento of my favorite composer, Sergei Rachmaninoff. It had a photo of him on the left, and on the right was an autographed letter. It was beautifully matted within a red and gold frame. The piece was bundled along with some original art work. I have no idea what happened to the bundle during the move, but it never wound up in the new place with everything else.
…and my BP meds. Fortunately, had to come back to retrieve our second car and found them in the trash.
When I moved to Phoenix, I had everything that I packed make it in one piece, nothing broken, nothing missing. Except for the power cord for my Sabtronics meter. Now, 34 years later, the meter is long gone, but I still think that some day (probably when I move into the Alzheimer’s ward) I will find it when I pack this house, and look in some hidden cranny where I stuffed it for the first move.
Somehow, all of my photos of the 1964 Alaska earthquake got left behind in one of my many military moves. Irreplaceable, of course.
I’ve left and given away 2 house and two dogs…I would love to have had the dogs.
I left my dignity somewhere in Las Vegas.
I left all my wood working tools at my ex’s in the garage when I got divorced. I was supposed to have them up in 6 months but drug my feet a couple months past the day. When I went to pick them up they were gone. Supposedly we were burglarized, her new bow friend happened to be a contractor. Maybe $2,000, all my mechanic tools of much greater value were still in place.
Didn’t realize how valuable at the time, but we had a fairly sizable collection of old glass projector slides from the silent movie days sitting in our cellar. Easily between 50 and 100. Not sure where we got 'em from - my dad probably picked them up at a flea market somewhere when I was a toddler. I thought they were neat, but left them there when we moved out.
Fast forward a couple of years and some fellow on Antiques Roadshow has a couple boxes on him; the expert tells him they were going for around $75 a pop at the time.
If you ever return, you’re likely to find it still there, untouched.
Big things I didn’t want to bother moving: a couch, a dryer, a freezer. It was easier to just leave behind the old one and buy a new one and have it delivered.
Of sentimental value mostly–a National Park Passport book with about 12 years worth of stamps.
Moved into a rental house, lived there three years. It wasn’t supposed to be that long, so there was a lot we didn’t unpack. When we left, we left behind a box that had some cookbooks and, I have no idea why, both my husband’s and my college diplomas. Because that’s where they fit, I guess.
We didn’t even know we’d left them there until three months later when the landlord dropped them off at our new place with a “thought you might need these” note. (Actually, we did not need these, but I at least was glad to have them back.)