A search in BibleWorks 7 for verses about both fasting and praying shows that combination occurs at least 11 times in the Bible:
Neh 1:4 And it came to pass, when I heard these words, that I sat down and wept, and mourned certain days, and fasted, and prayed before the God of heaven,
Psa 35:13 But as for me, when they were sick, my clothing was sackcloth: I humbled my soul with fasting; and my prayer returned into mine own bosom.
Dan 9:3 And I set my face unto the Lord God, to seek by prayer and supplications, with fasting, and sackcloth, and ashes:
Mat 17:21 Howbeit this kind goeth not out but by prayer and fasting.
Mar 9:29 And he said unto them, This kind can come forth by nothing, but by prayer and fasting.
Luk 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.
Luk 5:33 And they said unto him, Why do the disciples of John fast often, and make prayers, and likewise the disciples of the Pharisees; but thine eat and drink?
Act 10:30 And Cornelius said, Four days ago I was fasting until this hour; and at the ninth hour I prayed in my house, and, behold, a man stood before me in bright clothing,
Act 13:3 And when they had fasted and prayed, and laid their hands on them, they sent them away.
Act 14:23 And when they had ordained them elders in every church, and had prayed with fasting, they commended them to the Lord, on whom they believed.
1Co 7:5 Defraud ye not one the other, except it be with consent for a time, that ye may give yourselves to fasting and prayer; and come together again, that Satan tempt you not for your incontinency.
A quick scanning of these verses makes me think that we as believers today probably need to give more attention to this subject, especially given these references (Neh. 1:4; Dan. 9:3; Acts 13:3; 14:23; 1 Cor. 7:5).