I often see rabbits in cages with bottles of water hanging on the side. Can they drink from a bowl like a cat or a dog? Is there some reason they should drink from a bottle with a nipple?
Yes, rabbits can drink from a bowl. Currently, we have 5 pet rabbits; they all drink water from a bowl.
Water bottles are extensively used in rabbit production facilities. They don't take up space inside the small cage, they are easy to refill from the outside of the cage (without interacting with the rabbit). In fact you can purchase Rabbit Water Feeders for Automated System nipples that hook to a water line so you don't even need to go near the rabbit cage to change their water, BUT in regards to a pet rabbit, one that is a kept for companionship, this is a completely different situation. You want to spend time with your bunny; they are not to be locked in a tiny cage for their whole life. Your bunny is your friend.
Drinking from a bowl is the most natural way for a rabbit to drink. Selecting the correct bowl is important. A heavy ceramic bowl without a good place to for the rabbit to grip is important. Bunnies like to rearrange things and a light plastic bowl with bit of an edge is perfect for flinging across the room (even if it's not empty). Keeping the bowl away from the hay and litter box will help keep the water clean. Water bowls can go in the dishwasher, so they are easier wash the water bottles and nipples, which require bottle brushes.
If your rabbit has a large dewlap, it may get wet when they are drinking, so having something under the bowl to catch spillage may be important. We have two rabbits who live in our living room, who don't have dewlaps. They have a second water bowl on the carpet, next to the T.V., and water spillage is not an issue.