Cracked & sagging plaster is usually caused by water damage, either from leaking plumbing, or a leaking roof. If you have structural problems, like a settling foundation, you might see long diagonal cracks in the walls. If the damaged plaster is a smaller area, maybe 3 by 4 feet or so, then you might find a handyman who can repair the plaster, but if the damage is more extensive, it might be better to rip out all the plaster on the entire ceiling, and put up sheetrock.

"...if the damage is more extensive, it might be better to rip out all the plaster on the entire ceiling, and put up sheetrock."

Better or easier?
No drywall ceiling will have the sound charecterisitcs of a plaster ceiling.
Almst anything in plaster can be repaired, and it is not as difficult as it may appear.
If the finish surface has ben damaged it can be removed easily with a drywall knife and setting type drywall compound used to resotre the missing area. If you are in or near a large city lime and gaging plaster ae still available and you can reapirthe area the same way it was applied the first time.
If the damage goes deeper and there are cracks through the scratch coat (the next layer below the finish coat) you can use plaster washers to fasten it back tightly to the substrate and then bury them under a new finish coat.
The biggest differnec in plaster work from drywall is that plaster is not sanded during finishing. The finish coat is put on and tooled smooth. The trick is a trowel instead of the typical drywall knives.
For very large areas it gets a little tougher to create a smooth flat surface since there is no refernce to start from, but this is not usually a problem in repair work.

I was in panic mode when I saw some plaster cracks in my previous house (which I noticed just prior to selling), figuring that it was a major calamity.
Then I bought this house (1950's) and there are cracks everywhere :) Some I patched myself when I painted, others I just left for now.

I asked a lot of questions and did a lot of reading. Brickeyee's post capsulates it nicely. The best thing I read was something like: "(when dealing with plaster) expect to patch cracks every time you paint". Also, it is not uncommon for patched-up cracks to just crack again at a later time.

In other words, unless you have some major sagging or very deep cracks (or chunks falling off), no big deal. One article even mentioned that it adds a certain old-house charm :) In my case, a lot of cracking happened when new windows were installed, and I have a few in ceiling and door corners. Things would have to get a lot worse before I'd go through the trouble and expense of replacing the plaster with sheetrock.
(that said, if the cracks are substantial, I would hire someone who knows plaster well rather than a painter or someone used to dealing only with sheetrock).

The important things in your case, I'd think, is to make sure everything dried out quickly and completely after that leak.

In order to repair the cracks permanently, you are going to have to ensure that the plaster is solidly attached to the lath behind it (if not, the crack just comes back).

My advice is to do it yourself with a plaster adhesive--the job isn't too hard. You can always hire a handyman, but repairing plaster is easy to do yourself with the right tools.

You drill down to the lath with a masonry bit every 3 inches all along the crack, spray the holes with a conditioner, and then fill with your adhesive. After that, you temporarily clamp the plaster to the lath with screws and washers. Wait 24 hours, remove the screws and you are done! Your plaster is structurally reattached to the lath.

You can see how it works with the link below, or check out this old house:
http://www.thisoldhouse.com/toh/article/0,,1628100,00.html

Here is a link that might be useful: Plaster Repair

"In order to repair the cracks permanently, you are going to have to ensure that the plaster is solidly attached to the lath behind it (if not, the crack just comes back)."

Most plaster cracks are NOT caused by separation from the lath, but by movement of the structure over the years from settling.

Unlike drywall, plaster has zero 'give.'
If anything moves more than a fraction of an inch the plaster WILL crack.

Some cracks are 'seasonal,' caused by the expansion and contraction of a wooden structure.
They often open during the winter as the framing dries out and shrinks, then close for the summer when the humidity is higher and the wood expands.

The first thing to check is if you do have separation from the lath.
If you push on the plaster on each side of the crack and any give is felt you may have separation from the lath, or the lath itself may have pulled loose from the framing.

While there are methods of attaching the plaster back to the lath, it also needs to be pulled back into plane.
Simply filling the gap with glue is not going to fix the sag.
Plaster washers are the time tested method of securing plaster back to the lath and pulling it back flat at the same time.
They are then buried in a thin skim coat.

If there is no movement you should try and repair the crack.
If it returns you can try and determine why and make other repairs.

I use Durabond and mesh tape.
The mesh tape spans the crack but allows the Durabond to be forced through to fill the crack up.

Make sure you can dio a smooth job, since Durabond is as hard as old plaster and cannot be sanded very much, if at all.

Most of the old plaster was actual lime-plaster.
A mix of lime putty and gauging plaster.
The lime putty has a very long hardening time (think months to cure) but is very hard.
Gauging plaster has a very short set time.
The mixture has a moderate time without adding any further retarders to extend the set.