This list has all of the water rides at Disney World, not including the rides at the water parks, Blizzard Beach and Typhoon Lagoon. Some of the rides will get you wet, but most will not.
Kali River Rapids

Kali River Rapids is a water rapids ride in Animal Kingdom park. This is one of the water rides that you are sure to get wet on. So skip this if you want to stay dry, but it might be nice on a hot Florida day.
Living With The Land

Living With The Land is a relaxing ride in EPCOT that takes you through a greenhouse on a boat. You can see the full list of relaxing rides at Disney World here.
Gran Fiesta Tour Starring The Three Caballeros

Gran Fiesta Tour Starring the Three Caballeros is a boat ride in the Mexico Pavilion in EPCOT. This is another relaxing boat ride.
Frozen Ever After

Frozen Ever After is in the Norway Pavilion in EPCOT. You’ll board a Viking style boat and go through different scenes from the Frozen movie.
It’s A Small World

It’s A Small World in Magic Kingdom is a water boat ride that will not get you wet at all. You might have the catchy song stuck in your head for a while though.
Pirates of the Caribbean

Pirates of the Caribbean is a water ride that can get you a little wet, but not too wet. It has a small drop at the beginning of the ride that might spray you a little if you’re in the first couple of rows.
Na’vi River Journey

Na’vi River Journey is an Avatar themed ride in Pandora in Animal Kingdom. It’s another boat ride that you will not get wet on.
Tiana’s Bayou Adventure

Tiana’s Bayou Adventure is a newer ride in Magic Kingdom. You’re pretty sure to get wet on this ride, especially during the 5-story drop that sprays your log flume pretty bad. You can wear a poncho on the ride to combat this.
Jungle Cruise

The Jungle Cruise is a classic attraction in Magic Kingdom. You board a boat where your skipper takes you through a humorous tour of the jungle.
Liberty Square Riverboat

The Liberty Square Riverboat cruises around on the Rivers of America in Magic Kingdom. The riverboat and the river will be gone sometime this year or next though, as Disney has plans to add a Cars Land to Magic Kingdom in this area.