Yes and no.
Single-Family Units: No
If you live in a single-family dwelling, insulating between the floors may actually make your home colder. Hot air rises, and the heat produced on your first floor floats up to heat the second (and third) floors. This type of passive heat transfer saves you a bit of money on the energy bills.
My home was built in 1855, before the onset of central heating. I can only imagine how freezing cold it must have been in this house, with no insulation, no ducts and hot water pipes to transfer heat. Still, even after these inventions, the house was bitterly cold every winter because we had no insulation in the walls.
Well so far, I’ve managed to insulate the entire downstairs. It’s been a slow process since I’m gutting the house room by room. But it’s been SO worth it. The downstairs of this house is so cozy that I am hot during the winter. The upstairs, however, is still much cooler. The walls upstairs are uninsulated (for now). Yet because the downstairs of my home IS insulated, the rooms retain their heat and of course the heat rises. This year, for the first time EVER, we did not turn on the baseboard heaters this winter. The heat from the downstairs supplied all the heat for the upstairs. If my floors had been insulated, this would not have happened.
Insulating between floors does not save energy. It does not warm the house, but it does make the insulated section stay warmer longer. So all the data I have read says that insulating between floors is not necessary (and may even be detrimental) for a single-home dwelling.
Multiple-Dwelling Units: Yes
With that said, I think that the floors between multiple-home dwellings SHOULD be insulated. In this case, each family is paying for its own utilities. With the cost of fuel, the last thing a family living on the first floor wants to do is pay to heat the apartment on the upper floors. I once lived in an apartment for a few years. The heat was pretty expensive so we scrounged to conserve. Right before we we moving out, a neighbor confided to me that one of their rooms was on my heating line. I’d been paying to heat a part of the neighbor’s apartment for years, without ever knowing! Needless to say, we made tracks to chew out the landlord, lol.
How Do You Do It?
I heartily recommend that floors between apartment buildings are insulated. It can be a messy job, though. You can always rip out the layer of drywall, install fiberglass batting, and reinstall the ceiling. Another option is renting an insulation blower and filling the ceiling joist cavities with blown-in fiberglass insulation. A few notes on insulating between floors:
Do not fill the ceiling joists with insulation if the room has recessed lighting. Recessed lighting cans become extremely hot during use, and loose fill surrounding the can may ignite.
Do not insulate between walls or ceilings if your home still has the old knob-and-tube electrical wiring. Many building codes prohibit insulation with this wiring. The wiring, covered by insulation, can ignite and cause a fire.
It also helps to place the insulation blower outside a window, to reduce the dust and mess a blower makes. Most blowers are equipped with extra-long hoses for this purpose.
Thanks for reading!