My favorite prayer is likely the one I've said most recently. In The Church of Jesus Christ of Latter-day Saints, we have very few standardized or written/memorized prayers. We pray to thank our Heavenly Father for the specific blessings he has given us, and ask for the specific blessings that we desire, “according to His will.” We pray throughout the day; for example, a “typical” Mormon might have personal prayer morning and night, family prayer morning and night, and would say a prayer of blessing and thanks before meals (meal blessings are the prayers in which I find it most challenging to avoid “vain repetition”!)
We consider the Lord's Prayer to be the “perfect” prayer and the model for our own prayers; we don't regularly recite it as a prayer but would certainly consider that an appropriate part of personal or group prayer. Two of the few, set prayers we have can be found in The Book of Mormon, Moroni 4:3 and Moroni 5:2. These are the prayers said over the sacrament each Sunday in our worship service, consecrating the bread and water, reminding us of Christ's sacrifice for us, and committing us to follow Him.