Are there planes that can fly without wings? How would a plane be able to fly without wings?
There is a certain class of aircraft that are lifting bodies, which do not have wings but instead rely on airflow over a peculiarly-shaped fuselage to generate lift. However, this method is very inefficient and requires high airspeeds to make enough lift to support the plane. This means that the plane would have to carry an enormous engine to propel it, and its takeoff and landing speeds would be very high. 

Several experimental lifting-body planes were built and flown as gliders ~50 years ago for research purposes, and a search on lifting body will furnish you with more information on them.