I have removed quite a few ceilings for customers wishing to expose their floor joists. Depending on the age of the house, I usually try to discourage them doing it for a few reasons. By the age of your house, It's not a guarantee that the type of joist is what you would like to keep exposed. It may be that they are simply milled joists and resemble modern construction. They may be in less than great condition, having been drilled out for upgrades over the years, and there may well be wiring run through the joist pockets. Sadly, it was pretty common practice to hack into the floor above, to access the ceilings for wires, because the plaster was too time consuming to repair if opened up. I almost always use an inspection scope for a visual inspection before suggesting that it would be worth the time and expense for them to pull a good ceiling down, only to find a visual mess.
When it is possible and everything looks like it will be worth the effort, There is a good chance that you will have a constant mess from the floor above dropping dust and bits of "fluff" through the movement of the floorboards. In most cases, I do a short float from the underside of the floor, and install drywall between the exposed joists, fitting it carefully to each joist, and finishing the surface with a skim coat to try and replicate plaster. It's a very rare job that the joists and upper floor boards are of a quality worth keeping fully exposed. Unless you're in need of a new ceiling due to damage, I would highly recommend scoping every joist pocket and get a good look at what you're dealing with before tearing it down. It's a lot cheaper and easier to patch a few 1/2" holes than to replace the ceiling.
Owning an old home requires good stewardship, so that we can not only honor the original
craftsman who labored to build a home of enduring quality, but allow the next generations the opportunity to live in history.