Muslim couples do not generally recite vows but rather listen to the words of the imam, or cleric (although any adult male Muslim may officiate), who speaks about the significance of the commitment of the marriage and the couple's responsibilities toward each other and Allah. The bride and groom are asked three times if they accept each other in marriage according to the terms of their traditional marriage contract, or Nikah. Then they sign, the marriage is sealed, and the gathered congregation may bless them.
However, some Muslim brides and grooms do choose to also exchange vows. Here is a common (quite traditional) recitation:
Bride: "I, ______, offer you myself in marriage and in accordance with the instructions of the Holy Koran and the Holy Prophet, peace and blessing be upon him. I pledge, in honesty and with sincerity, to be for you an obedient and faithful wife."
Groom: "I pledge, in honesty and sincerity, to be for you a faithful and helpful husband."
Want to write your own wedding vows? Make sure your officiant will accept personalized vows, and get started by asking yourselves these 20 questions.
Wedding Ceremony + Wedding Vow Ideas