Amateur wrestling requires incredible speed, endurance, strength, and skill, especially at the higher levels.
"Professional" wrestling is harder to talk about, because there are so many different styles and types of wrestlers. In general, though, technical-style wrestlers and MMA-style wrestlers need to be in excellent shape (Benoit, Guerrero, Angle, American Dragon and Low Ki all come to mind) whereas brawlers and "garbage" wrestlers will usually not have the best conditioning (think Sandman, Bradshaw, and Kevin Nash).
High fliers and luchadores are mostly in good shape, except for Jeff Hardy, but Jeff Hardy sucks anyway.