Yes, most cruise lines allow you to bring a stroller onboard. Strollers, prams and other mobility equipment such as wheelchairs, walkers and knee scooters are common sights on cruise ships.
If you are bringing a stroller, choose something compact and collapsible if possible. Cruise ship hallways can be narrow and stateroom doors are often much smaller than the doors you are used to at home. A lightweight umbrella or travel stroller is usually much easier to maneuver around the ship.
A double wide stroller is best left at home. Besides being difficult to get through doorways, it can be cumbersome in crowded elevators, restaurants and busy hallways. If you need a stroller for two children, a narrow tandem model will generally be much easier to manage.
Keep in mind that you will need to store the stroller inside your stateroom when you are not using it. You cannot leave it in the hallway outside your cabin where it could obstruct the passageway. A stroller that folds down small enough to tuck into a closet or corner of the room can make a big difference in an already compact cruise cabin.