Selfless- All decent catchers are selfless. Whether it's taking one for the team and holding onto the ball while getting mowed down by a runner. Or little things like letting pitchers get all of the glory for a no hitter.
Quick Thinking- Quick Thinking is required for "framing" pitches. (making them appear closer to the strike zone). Quick Thinking also requires reacting to where the ball is hit and letting people know where it should go.
Should be Right Handed- Most catchers are right handed. The reason for this is on a throw from the outfield a left handed catcher would have to catch it at a weird angle, making the tag almost impossible.
High pain tolerance- Baseballs to the chest, jammed fingers, heavy gear, and jacked up knees; to name a few. Catchers need to be tough all around.
Talkative- being talkative to both the umpire and the other team are huge roles. Building relationships with umpires never hurts and most of the time, helps. And nothing's wrong with a little trash talk to the other team.
Good Communicator- Communication is key. Not just chatting with the umpire; but letting the team know where they're going, settling down a pitcher here and there, and letting coaches know what you see going on are huge roles to take in as a Catcher.
Great Arm- Most great Catchers have an absolute cannon for an arm. This is essential for hosing down kids that are trying to steal.