The correct answer is - the Atlantic Ocean.
If South and Southeast Asia are excluded, then the moistest places on the Earth are influenced by the Atlantic Ocean. This places are the Amazon basin, the Caribbean islands, southern half of Central America, the east coast of North America, Western Africa, Ireland, and the British Islands. All of this places are very moist and it is a direct result of the Atlantic Ocean which has warm and moist currents that deliver the moisture in all of this places.