In North America the refrigerator and clothes washer/dryer are usually the landlord's, but sometimes people own their own clothes stuff -- I think self-ownership is becoming less common with time, but only have anecdata to back it up.

If I ever rent out my place it will absolutely include the appliances (fridge, stove, dishwasher, washing machine) and probably some bits of furniture like bookcases, because it'd take a whole team of people working for half a day to get it all down 4 extremely tight flights of stairs, and that's half the depreciated value of it all right there anyway.

Washer/dryer is often included, because the law states that if there isn’t a suitable outdoor area, some sort of drying facility must be supplied. (In VIC it does, anyway.)