Although cruises allow infants and toddlers they don't necessarily cater to them. Some cruise lines provide playpens or cribs upon request but only have a limited amount aboard so be sure to request in advance.
Disney Cruises are most accommodating of families, they provide complimentary Pack-N-Play cribs, strollers, bottle warmers, bottle sterilizers, and allow fresh pureed vegetables to be prepared in the dining room or by room service upon request.
While Carnival has strollers, both single and double, for rent most cruise lines do not so be sure to bring your own. You can find Carnival's rental fees here.
All cruise ships are equipped with high chairs in the dining areas.
Bring enough diapers for your entire cruise. I made the mistake on our first cruise with my oldest thinking I could buy diapers on board and save the space in my luggage especially since we flew into the city of our port departure. Big mistake as our ship Royal Caribbean Rhapsody of the Seas, did not sell diapers or wipes on board. I had to waste time at our stop in Santorini to search for a pharmacy to purchase some, not how I wanted to spend my time on that beautiful island. While there are some cruise lines that do have diapers/wipes for purchase on board they are generally extremely overpriced.
Even if your child has never gotten diaper rash I would strongly recommend bringing diaper rash cream with you. You are going to be very busy especially on port days if you do a shore excursion. You may be riding in a van/bus for hours and may not able to change your babies diaper as often as you are used to doing. Again this is something they might not sell on board so better to be safe than sorry.
For specifics on each cruise line click on the links below: