Replace it. Hanging sheetrock is really not that hard, and easier than a lot of messy patching work, in my opinion.
Depending on just how bad of shape its in will determine your choices.
A textured paint can be applied to hide some issues. If its really bad and your not willing to put the effort into spackle and elbow grease to make it smooth again. You can popcorn finish it. This texture was used a lot, and I admit I used it in my home. You will find lots of people on this site asking how to remove it. But it does hide a ton of issues. The power with the foam balls are mixed with a titanium oxide as a whitening agent. You add water and rent a compressor and spray unit. Then once mixed it simply gets sprayed onto the ceiling. When it drys a few hours later it is bright white and looks great. It is fragile however so no bouncing balls on the ceiling or it will come off. It can be removed very easy with just a putty knife. If you desire to have a more durable result then mix the material with paint. Its very messy to apply so be sure you mask everything up well and cover everything with plastic. Or it will become covered with the over spray. But if you do get it on stuff, it can be cleaned easy with water. Unless you mix with paint.
Still another idea is to use the metal ceiling panels that simply glue or nail onto the ceiling. It gives the room a old style look but will hide any issues with quality of the ceiling.
Then there is good old suspended tiles if you are into the industrial look.
Sectioned tin ceilings are pretty cool looking too. But you may need to match the rest of the decor in your home.
if it's in bad shape it may be less costly just to replace it. i do drywall alot. and would suggest that you replace it. if it's damaged from water leaks you may have mold growing on it. it is not that hard to replace drywall in the ceiling.
It's a rental, so trying to keep cost down. Sheetrock not damaged by water, just a older home. We're completely remodeling the kitchen, with new cabinets, countertops & stanless appliances.
screw up any areas suspected of sagging,cut and tear off tape, retape ,mud and sand.If not satisfied with that ,use a mix of mud and latex paint ,with a little tint and apply liberally.Looks better than old popcorn.Cheap alternative to faux finish .
For a rental, if you don't want to invest the time and money to redo and make it perfect, I would second Woodbridge's recommendation, and slightly amend it. You can rent compressors and spray on texture for a more contemporary textured finish than the old, much maligned popcorn look. Warning though. It's messy, so cover everything well, and definitely do all this before putting in any of your new cabinets, appliances, etc.