Called the Lord's Prayer, as it was the one taught/recited by Jesus himself to the people when asked how to pray.
Depending on which church you find yourself in, even if part of the same religion(well, generally Christianity of course), or denomination, you will find variations. They all mean the same thing of course. The difference is all just diction, choice of words. I could be in two different Catholic churches, merely 20-minutes' distance apart, and still have to sing the 'Our Father' in the Mass differently.
I normally have it memorised which church sings what. That is also why, whenever in a new church, one you haven't been to previously, always sing softer than other people, so you won't assume, make a loud mistake, and embarrass yourself in front of the congregation, and therefore exposing your non-belonging to said church.
Which variation to use, usually depends on the already officially chosen one by the particular church(but this is normally only with regards to the singing of the prayer during the Mass itself, it's not forced on everyone in the church for use all of the time), or on the word preference of the majority of people whom you are saying the prayer with.(sometimes majority of people means the guy with the loudest voice, or quickest to the point)
Where I'm from, they have a slightly simpler form of the prayer, especially useful when getting children to remember, or simply, get used to the words. Also seems to be sort of a lowest common denominator among the variations.
It seems like long, old, or slightly-more-complexed words are being phased out in favour of shorter, modern, direct, easier-to-understand ones. Yes, the others aren't that complexed/archaic anyway, but, i don't know! Let's just say, it's easier than the others, eventhough the others aren't that difficult in the first place. Words like 'hallowed' become 'holy', 'temptation' becomes 'test', and 'trespass', 'sin'. That is,
Our Father in Heaven,
Holy be Your name.
Your kingdom come,
Your will be done,
On Earth as it is in Heaven.
Give us today our daily bread,
And forgive us our sins,
As we forgive those who sin against us.
Do not bring us to the test,
But deliver us from evil.