Do it! You won't be sorry. They make special sound-dampening insulation and drywall. Your place will look brand new...smooth, flat walls with no cracks and no sounds of plaster sliding down the inside of the wall when you hang a picture hook.

Do it. I have done the same because in the past I replaced plaster with plaster, and now I see micro cracks because the plaster expands and contracts with the seasons (humidity/really dry). Be aware that plaster and lathe has a different thickness than drywall.

if you are willing to use some sq footage you can have the existing wall firred our and apply the same sound dampening insulation and drywall on top of that if you want more insulation. why totally ruin the original plaster?

I agree. Do it. We did and our house is quiet & toasty warm. I'm also pretty sure that getting rid of all that horse hair in the lath reduced our allergies.

Instead of tearing out your side of the adjoining wall, you can cut modest sized holes up near the top of the wall in each space between the studs and blow new insulation in to fill the gap between the studs.

I agree with those above that say Do IT! I have plaster walls all over my house and I tear them down whenever I have the excuse. The insulation makes such a difference, and drywall is so much easier to deal with when painting, hanging things, dropping cables, etc. But if you are doing this yourself, I cannot emphasize enough to wear a heavy-duty face mask and protective clothing. The plaster dust also gets everywhere, so be sure to cover everything or hang drop cloths to protect your home.

Drill holes at the top and blow in the insulation.

i agree with the "do it" comments. my plaster walls drive me crazy. just make sure you prepare for the tons and tons of dust you will get with the plaster. proper prep will go A LONG way in keeping your sanity! be sure to seal the room as best you can to contain the dust (again, as best you can ;))

Do it. We had to replace p&l with drywall in our bungalow and never regretted it. As others have noted, be prepared for a hellacious mess when you demo. And that your trim boards will be too short if you don't shim the drywall out about 1/2" from the studs. (1/2" drywall vs. 1" p & l composition)

If the two apartments share studs, you're going to be disappointed if you just pull off the plaster and put in insulation. You can either put up your own floating wall (best solution) and then drywall that. Or use two layers of drywall with stuff called Green Glue between them for an easier method.

check your local building codes and see what they require as fire breaks between units.

In addition to fire breaks, I recommend talking to an engineer about whether the closet wall is load-bearing. An engineer could also probably advise on sound proofing.

Lead poisoning is a serious health issue. If the plaster is older than 1972, be aware that demoing it will produce lots of airborne dust, which will contain lead from years of lead-based paint - bad for adults and very, very bad for children and pets.

To add to the what @lella said-- not only is there lead, but the horsehair was also treated with arsenic.

One really important point to check on- has your wiring been updated? If you have any knob-and-tube wiring in those walls you'll need to replace it before you insulate. The old wiring depends on the air space to disperse heat, and it creates a fire hazard if you surround it with insulation. Also note that some of the old framing techniques were different than today's- our 1908 house has balloon-framing, where there is a continuous open space from the 2nd floor down through the first. If that's the case for you, you would want to make sure that the wiring is replaced on the floors below you and then either put on some kind of block between floors or end up insulating all the way down.
I'm personally undecided about plaster vs drywall--in our house, the previous owner's poor taping job on the drywall looks far worse than the plaster that needs repair, and the drywall certainly performs far worse when it gets damp (basement in particular).

blow in the insulation.

I completely agree with taking down the plaster and putting in the insulation and drywall... if you can! I'm all for keeping original what was original as long as it suites your needs, and plaster with no insulation apparently does NOT suit anyone's needs in an apartment building, whether neighbors are loud or not. I also agree with the other comments about possibly getting a professional or doing your research REALLY well to know how to do it correctly and switch everything that needs to be switched and updated in the process

Do it, but make sure they're not load-bearing walls before you knock them down.

Do something. Beware the asbestos (still being exported by Canada, with the support of the ruling junta of Steven Harper, but against the wishes of the population) and other toxins they used to use.

I say do it; I've torn out some of my plaster walls and I'm slowly working up to tearing out the rest. My preference is to replace the plaster with drywall of similar thickness (my plaster is 3/4" thick, so 3/4" drywall works well; for 1" plaster use two sheets of 1/2" drywall) to give the same sound-dampening qualities. (Mass cuts noise transmission; you can also get drywall designed to cut down noise transmission even more than the regular stuff.) That will also help with fire protection between the units.

FYI, lead paint was almost never used on interior walls; it's mostly on trim and exteriors. But most paint stores sell little test kits.

Be really careful, I've seen/heard horror stories from people tearing the lathe and plaster off of one wall, only to have the other side of the wall crumble as well and I don't think your neighbors would appreciate that.

Unfortunately I was not persuasive enough with my landlord, who will not let me be tearing down walls anytime soon. Which is now even more depressing seeing that you all agree with me to do it! Maybe I should foreword her the link to this page!

I'm not sure it was clear that this wasn't your property or that you hadn't actually run any of your ideas by your landlord first. Otherwise, I think there would have been a lot more of, "Make sure your landlord is okay with this...then do it."

And I don't know that I'd recommend doing that in a rental.

Don't tear it down. Build another wall in front of the plaster. You will lose 4" for the frame, and 1/2" for the sheet rock. No surprises, and it will be much quicker and skip all the demo costs.

I second green glue, not from experience but from a lot of research that I've done

Don't do it. In contrast to most of the posters, I have a different opinion. The original plaster has a nice look to it (not perfectly smooth, but that matches my life). It is a *better sound and heat insulator than a single layer of drywall, so to increase the sound and heat insulation you need to take additional steps (as people have mentioned). The lead is a serious issue, and contractors can't remove it anymore in MA without training on lead containment - they are taking it that seriously. You can ADD a layer of drywall on top of the plaster, adding to the insulation, making it smooth and pretty if it is totally cracked. my understanding is that adding blown in insulation will not dampen noise. A friend of mine collects old pieces of drywall and slips them into the gaps which increases the mass between the two spaces (hello, 10th grade physics!) I am a landlord, too, and I would say No to a tenant who wanted to do this, for the above reasons. Sorry that the fix is not easy. Good luck.

I want to be supportive, but I'm amused/amazed that you'd think knocking down walls as a renter is a viable option. The liability the landlord would be taking on, both in terms of injury to you and to the house is showstopping, not to mention that this simply is not your property. Yikes.