Yes, you still can on Carnival.
Carnival Policy: "In many ports, guests have the option of carrying luggage on board at embarkation and off the ship at the end of the cruise as long as it does not exceed 16"H x 24"W x 30"L."
I haven't heard of a port where they don't allow it but their policy suggests it's a possibility that some ports may not.
Just remember your cabin may not be ready for some time after you board and you may be lugging it all around with you for some time (up/down stairs, elevators, etc). You always see people who carry it all on and typically the looks I've seen on their faces are "Why didn't we just check this in!?".
Checked bag limit for Carnival is two suitcases per person, with each suitcase not to weigh more than 50 pounds and not exceed 16"H x 24"W x 30"L.