Here's a definition of faith:

(Hebrews 11:6 NIV) And without faith it is impossible to please God, because anyone who comes to him must believe that he exists and that he rewards those who earnestly seek him.

And here's an excellent example of it in action:

(Mark 1:40-42 NIV) A man with leprosy came to him and begged him on his knees, "If you are willing, you can make me clean." {41} Filled with compassion, Jesus reached out his hand and touched the man. "I am willing," he said. "Be clean!" {42} Immediately the leprosy left him and he was cured.

And despite healing a different man, Jesus had a stern warning for him:

(John 5:12-14 NIV) So they asked him, "Who is this fellow who told you to pick it up and walk?" {13} The man who was healed had no idea who it was, for Jesus had slipped away into the crowd that was there. {14} Later Jesus found him at the temple and said to him, "See, you are well again. Stop sinning or something worse may happen to you."

Not everyone with faith is righteous.