“Ask, and it will be given to you; seek, and you will find; knock, and it will be opened to you. For everyone who asks receives, and he who seeks finds, and to him who knocks it will be opened.” Matthew 7:7-8

“And all things you ask in prayer, believing, you will receive.” Matthew 21:22

“This is the confidence which we have before Him, that, if we ask anything according to His will, He hears us. And if we know that He hears us in whatever we ask, we know that we have the requests which we have asked from Him.” 1 John 5:14-15

“Then you will call upon Me and come and pray to Me, and I will listen to you.” Jeremiah 29:12

“It will also come to pass that before they call, I will answer; and while they are still speaking, I will hear.” Isaiah 65:24

“You will pray to Him, and He will hear you; and you will pay your vows.” Job 22:27

“In that day you will not question Me about anything. Truly, truly, I say to you, if you ask the Father for anything in My name, He will give it to you. Until now you have asked for nothing in My name; ask and you will receive, so that your joy may be made full.” John 16:23-24

“Therefore, confess your sins to one another, and pray for one another so that you may be healed. The effective prayer of a righteous man can accomplish much.” James 5:16

“Whatever you ask in My name, that will I do, so that the Father may be glorified in the Son. If you ask Me anything in My name, I will do it.” John 14:13-14

“If you abide in Me, and My words abide in you, ask whatever you wish, and it will be done for you.” John 15:7

“But you, when you pray, go into your inner room, close your door and pray to your Father who is in secret, and your Father who sees what is done in secret will reward you.” Matthew 6:6

“Call upon Me in the day of trouble; I shall rescue you, and you will honor Me.” Psalm 50:15

“Then you will call, and the LORD will answer; You will cry, and He will say, ‘Here I am.’” Isaiah 58:9

“The LORD is far from the wicked, but He hears the prayer of the righteous.” Proverbs 15:29

“He will call upon Me, and I will answer him; I will be with him in trouble; I will rescue him and honor him.” Psalm 91:15

“If you then, being evil, know how to give good gifts to your children, how much more will your Father who is in heaven give what is good to those who ask Him!”  Matthew 7:11

“The righteous cry, and the LORD hears and delivers them out of all their troubles. Psalm 34:17

“Evening and morning and at noon, I will complain and murmur, and He will hear my voice.” Psalm 55:17

“The LORD is near to all who call upon Him, to all who call upon Him in truth. He will fulfill the desire of those who fear Him; He will also hear their cry and will save them.” Psalm 145:18-19

“So do not be like them; for your Father knows what you need before you ask Him.” Matthew 6:8

“Whatever we ask we receive from Him, because we keep His commandments and do the things that are pleasing in His sight.” 1 John 3:22

“Call to Me and I will answer you, and I will tell you great and mighty things, which you do not know.” Jeremiah 33:3

“Therefore I say to you, all things for which you pray and ask, believe that you have received them, and they will be granted you.” Mark 11:24

From http://www.intouch.org/resources/gods-promises/content/topic/prayer