Psalm 34:17-20:

The righteous cry, and the LORD heareth, and delivereth them out of all their troubles.
The LORD is nigh unto them that are of a broken heart; and saveth such as be of a contrite spirit.
Many are the afflictions of the righteous: but the LORD delivereth him out of them all.
He keepeth all his bones: not one of them is broken.

Notes on Psalm 34:17-20:

Do you consider sickness to be a trouble?  Then consider that the Lord delivers you out of all your troubles, including sickness.  Do you consider sickness to be an affliction?  Then consider that the Lord delivers you from all your afflictions, including sickness.

Note that there are two other characteristics of the people being delivered in this passage.  They are humble, and they cry to the Lord for deliverance.  Healing is not automatic.  It does not just happen to you because it is the will of God.  You have to receive it!

This is the verse I would be meditating on if I ever broke a bone.  God promised the righteous no broken bones, so if one is broken, you have the right to receive healing for it.

See also:

Objection: Many Are the Afflictions of the Righteous
Objection: Jesus Could Not Have Borne Broken Bones on the Cross Because Not One of His Bones Was Broken (John 19:36)
Condition: Broken Bones