It is God's will to heal people.  It is a part of the atonement; one of the blessings Jesus died to provide to us.  

Isaiah 53:4 (KJV) says:

Surely he hath borne our griefs, and carried our sorrows: yet we did esteem him stricken, smitten of God, and afflicted.

Griefs in the Hebrew means sicknesses and diseases.  The word sorrow in the original language means pains.  Jesus bore every sickness, disease and pain on His body at the whipping post and on the cross.

Isaiah 53:5 (KJV) says:

But he was wounded for our transgressions, he was bruised for our iniquities: the chastisement of our peace was upon him; and with his stripes we are healed.

In the Hebrew, wounded means pierced, and bruised means crushed.  So, verse 5 says that He was pierced for our transgressions, and He was crushed for our iniquities.  The word chastisement means punishment, so it is saying that the punishment for our peace was upon Him, and with His stripes, or His bruises, we are healed.  

In Isaiah 53:5, we see healing for all three parts of mankind; spirit, soul, and body.

For our spirits:

He was wounded for our transgressions and bruised for our iniquities.

For our souls:

The chastisement of our peace was upon Him.  He took our torment, stress and anxiety and gave us His peace.

For our bodies:

With His stripes we are healed.  This covers physical healing.  Jesus was physically whipped and then nailed to a cross.  With the wounds He bore, we are healed.

Isaiah 53:4, 11-12 (KJV):

Surely he hath borne our griefs, and carried our sorrows: yet we did esteem him stricken, smitten of God, and afflicted... He shall see of the travail of his soul, and shall be satisfied: by his knowledge shall my righteous servant justify many; for he shall bear their iniquities. Therefore will I divide him a portion with the great, and he shall divide the spoil with the strong; because he hath poured out his soul unto death: and he was numbered with the transgressors; and he bare the sin of many, and made intercession for the transgressors.

The same Hebrew word for bear and carried is used to describe both our sins and sicknesses.  Jesus not only bore our sins, but our sicknesses as well.  He took our sins and gave us His righteousness.  He took our sickness and gave us His healing and health.  And He took our poverty, and gave us His physical, literal riches (II Corinthians 8:9)

Galatians 3:13-14 (KJV) says:

Christ hath redeemed us from the curse of the law, being made a curse for us: for it is written, Cursed is every one that hangeth on a tree: That the blessing of Abraham might come on the Gentiles through Jesus Christ; that we might receive the promise of the Spirit through faith.

We have been redeemed from the curse of the law, which is poverty, sickness, and spiritual death.  And now we can receive the blessing of Abraham: prosperity, healing/health, and eternal life.

Christ paid for our healing.  As we read in Isaiah, it was prophesied ahead of time.  Jesus walked in healing power throughout his earthly ministry (Matthew 8:16-17).  Jesus fulfilled Isaiah's prophecy at the cross, and Peter tied it all together for us in I Peter 2:24.

The sacrificial death of Jesus, the atonement, bought our salvation, healing and prosperity.  Therefore, we have just as much right to be healed as we do to be saved.