Before moving to Japan, I lived in a land of free boxes called Portland, Oregon. On every curb or corner, you might find a box marked FREE and filled with old clothes and other used items. The thinking there is that someone might be able to use some free used clothes or repurpose them for some sort of project. Same goes for furniture and other items which a sign can be taped to. It's kind of like a fun treasure hunt where you might find something great for free.
In Japan not so much. The idea of a garage sale in Japan is absurd and even swap meets and recycle shops are approached with caution. This mentality seems to be slowly evolving, because getting the thing you need for less isn't such a bad idea. (I still don't expect to see free boxes on the side of the road in Japan any time soon.)
この (ハンガー) は ご自由に お持ち下さいませ。
kono (hanga-) wa go jiyuu o mochi kudasaimase.
Please take these (hangers) freely.
When a box says this, it means the (hangers/what's in the box) is free.
Need some hangers? Check a dry cleaner. Clothing stores might have extras from time to time also, and some locations seem to always have a free box of hangers. They're a little nicer than what you'd find at the 100 yen store too.
There aren't lines of people picking up the free hangers, but I'm happy to see that it's an acceptable way to pass on perfectly useful items.
From my perspective, Japanese people usually take good care of things and are incredibly resourceful. Especially the older generations who didn't always have the 100 yen stores to rely on. I don't encourage hoarding, but reusing things instead of throwing them away then buying something new makes sense financially and environmentally.
At the same time, I see a lot of trash and recycling from the neighbors every week when I take mine out. I sometimes have to resist looking through things in the recycling piles so I don't look like the crazy foreign lady. Used clothing, books, magazines... kind of want to look through but... it isn't really something most people do here. I have a feeling it does happen, but only when no one is looking (I've seen clean 'trash' disappear before the pickup time).
(Back home, peeking at what others have thrown out is a side hustle for some - picking up deposit recyclables or broken items that can be repaired and sold.)
What about when you're moving and have some still-useful items you don't want anymore?
Putting out your own free box in Japan is prolly not going to go well.
Proper disposal in Japan is tricky, even for the things you want to throw away that don't fit neatly into the usual trash and recycling routine.
A lot of foreigners use the “Sayonara Sale” free advertisements online, but that only works if you live in an urban area. 'Giving' or selling items to the recycle shops sometimes works, although I was asked to pay a fee for each (working) item 'recycled' when I asked someone driving the truck around collecting items. If we put larger items into the trash area, usually we have to pay a fee and schedule a pickup. Maybe it's best to keep in mind how we'll dispose of things and the cost to do so before even buying them?
For anything in good condition, I've found the best way to pass it on was find a friend who wanted it. Preferably a friend who lives nearby and owns a car. With some jobs, the housing and some household items are provided, so they are passed on to the next employee and you won't have to worry about this too much.
Recommended: Author of "Everyone Poops," (五味太郎) Gomi Taro's awesome picture book, (正しい暮らし方) "The Correct Way of Living," in which the correct way to separate your trash is discussed.