The reason for Undertaker hiding the face is that he had a facial injury. He wore a Phantom mask for this. The gimmick lasted till Diesel unmasked him at the 1996 Royal Rumble.
Oney Lorcan unmasked Elias after defeating him in a must-win match. After this, the company decided to drop his masked role for unknown reasons and their are endless speculations around it.
CM Punk lost to Rey Mysterio at Over The Limitt and then Rey shaved Punk's head. So, to conceal his baldness, Punk started wearing a black mask .
Upon his return to WWE after battling acromegaly disease in 1986, Andre didn’t show up for a game which led to him getting banned. The fear of shame led him to start doing masked stints in the game.
In 1996, he and his family started wearing red-colored masks. Rishiki, however, ceased to impress the crowd. After a long while, he dropped the masks after only one successful game against Rocky Maivia.