Matthew 6:16-18
"Moreover when you fast, be  not, as the hypocrites, of a sad countenance: for they disfigure their faces,  that they may appear unto men to fast. Verily I say unto you, They have their  reward.  But thou, when thou fastest, anoint thine head, and wash thy face; that  thou appear not unto men to fast, but unto thy Father which is in secret: and  thy Father, which seeth in secret, shall reward thee openly."

Matthew 17:18-21
"And Jesus rebuked the devil; and he departed out of him: and the child was cured from that very hour. Then came the disciples to Jesus apart, and said, Why could not we cast  him out? And Jesus said unto them, Because of your unbelief: for verily I say  unto you, If ye have faith as a grain of mustard seed, ye shall say unto this  mountain, Remove hence to yonder place; and it shall remove; and nothing  shall  be impossible unto you.  Howbeit this kind goeth not out but by prayer and  fasting."

Luke 2:37
"And she was a widow of about fourscore and four years, which departed not from the temple, but served God with fastings and prayers night and day."

Acts 13:2
"And when they had fasted and prayed, and laid their hands on them, they sent them away."