From Ministration to the Sick (BCP p. 456)

N, I lay my hands upon you in the Name of the Father, and of the Son, and of the Holy Spirit, beseeching our Lord Jesus Christ to sustain you with his presence, to drive away all sickness of body and spirit, and to give you that victory of life and peace which will enable you to serve him both now and evermore. Amen.

or this

N, I lay my hands upon you in the Name of our Lord and Savior Jesus Christ, beseeching him to uphold you and fill you with his grace, that you may know the healing power of his love. Amen.

and/or this

N, I anoint you with oil in the Name of the Father, and of the Son, and of the Holy Spirit. Amen.

and/or this

As you are outwardly anointed with this holy oil, so may our heavenly Father grant you the inward anointing of the Holy Spirit. Of his great mercy, may he forgive you your sins, release you from suffering, and restore you to wholeness and strength. May he deliver you from all evil, preserve you in all goodness, and bring you to everlasting life; through Jesus Christ our Lord. Amen.

Adapted from Prayers and Thanksgivings (BCP p. 831)

55. For a Person in Trouble or Bereavement

O merciful Father, you have taught us in your holy Word that you do not willingly afflict or grieve humankind: Look with pity upon the sorrows of your servant for whom our prayers are offered. Remember him, O Lord, in mercy, nourish his soul with patience, comfort him with a sense of your goodness, lift up your countenance upon him, and give him peace; through Jesus Christ our Lord. Amen.

56. For the Victims of Addiction

O blessed Lord, you ministered to all who came to you: Look with compassion upon this person who through addiction has lost his health and freedom. Restore to him the assurance of your unfailing mercy; remove from him the fears that beset them; strengthen him in the work of his recovery; and to those who care for him, give patient understanding and persevering love. Amen.

From Thanksgivings for Family and Personal Life (BCP p. 841)

11. For the Restoration of Health

Almighty God and heavenly Father, we give thee humble thanks because thou hast been graciously pleased to deliver from his sickness thy servant N, in whose behalf we bless and praise thy Name. Grant, O gracious Father, that he, through thy help, may live in this world according to thy will, and also be partaker of everlasting glory in the life to come; through Jesus Christ our Lord. Amen.

From Common Worship (Church of England)

In the name of God and trusting in his might alone, receive Christ's healing touch to make you whole. May Christ bring you wholeness of body, mind and spirit, deliver you from every evil, and give you his peace.  Amen.

(click here for full section: Wholeness and Healing)