Debtors vs. Trespassers

The answer to this question, and it is a very good question, requires a deep understanding of the social, economic, and theological history of Europe. The key question to ask is the difference in meaning between debtors and trespasses.

Usury was against church law, and so Christians were barred from charging interest. Judaism had no such law, so European monarchs and rulers encouraged Jews to immigrate to their areas of control as far back at the 12th Century to better facilitate commerce, and so Jews became the banking class across Europe. Indeed, the Age of Exploration could not have happened but for the Jewish diaspora.

The Enlightenment and the rise of Liberalism brought about significant change, especially the dramatic rise of the Merchant Class. Usury laws were challenged to free the emerging industrial class in their pursuit of profit, and "debtors" was changed to "trespasses." The idea of forgiving debts was an anathema to Christians seeking monetary wealth, and the desire to protect and make sacred private property drove this change.

I am providing a very superficial account that led to the change, and it was a change to Protestantism in particular. One needs to understand the impact of the Black Death upon Europe, the impact of the Reformation, the impact of the Age of Exploration, the impact of the Enlightenment, and several other factors.

The bottom line is that the change was made to allow Protestants to increase their wealth. It's a fascinating evolution, but understanding requires a great deal of study, but study that is worth the effort.

So being christened United Methodist and confirmed United Presbyterian now (PCUSA) I have mostly seen debts. I have attended some Presbyterian churches that use sins instead of debts. I think its just all semantics. But like Peter Turner mentioned above, in the Latin, which is the official language of the Catholic Church and Vatican, you will notice it is debts:

Panem nostrum quotidianum da nobis hodie, et dimitte nobis debita nostra sicut et nos dimittimus debitoribus nostris.

The Greek is phrased slightly differently in Matthew, Mark, and Luke. (Another answer has already compared Matthew and Luke). Following the King James for the English translation:

Matthew 6:12

και αφες ημιν τα οφειληματα ημων ως και ημεις αφιεμεν τοις οφειλεταις ημων

And forgive us our debts, as we forgive our debtors.

Mark 11:25

και οταν στηκητε προσευχομενοι αφιετε ει τι εχετε κατα τινος ινα και ο πατηρ υμων ο εν τοις ουρανοις αφη υμιν τα παραπτωματα υμων

And when ye stand praying, forgive, if ye have ought [i.e. anything] against any: that your Father also which is in heaven may forgive you your trespasses.

Luke 11:4

και αφες ημιν τας αμαρτιας ημων και γαρ αυτοι αφιεμεν παντι οφειλοντι ημιν και μη εισενεγκης ημας εις πειρασμον αλλα ρυσαι ημας απο του πονηρου

And forgive us our sins; for we also forgive every one that is indebted to us. And lead us not into temptation; but deliver us from evil.

An early Christian document dating from the first century - The Didache - prescribes the Lord's prayer to be said three times each day. The version that appears in The Didache uses the word for "debts" (οφειληματα) rather than trespasses (παραπτωματα). (It seems that there are two variants - one that contains the phrase "as we forgive our debtors", and another that does not). The Liturgy of St. James, which is the oldest eastern Liturgy still used also uses the term for "debt" rather than "trespass".

The Latin Vulgate versions of the Gospel texts seems to slightly blur the distinction that is in the Greek. In Matthew, debitum is used for ὀφείλημα ("debt"), with debenti being the "debtors"; in Mark, peccatum is used for παράπτωμα ("trespass"); in Luke, peccatum is also used for ἁμαρτία ("sin"), with debenti again being "every one that is indebted". The Douay-Rheims translation of these verses is:

Matthew 6:12

And forgive us our debts, as we also forgive our debtors.

Mark 11:25

And when you shall stand to pray, forgive, if you have aught against any man: that your Father also, who is in heaven, may forgive you your sins.

Luke 11:4

And forgive us our sins, for we also forgive every one that is indebted to us. And lead us not into temptation.

In view of all this, and in support of what another has answered, I don't think there is a Catholic and non-Catholic wording issue here. There are Roman Catholic sources (e.g. Douay-Rheims Bible) that use "debts" and "sins" in place of "trespasses", and "debtors" and those "indebted to us" in place of "trespassers". It amounts to which underlying Greek source is implied and how the Greek and/or Latin is rendered into English by the translator.

Being raised Catholic, I was taught trespasses vs debtors. As a child, I was also taught to use the shorter version without:

For thine is the kingdom, and the power, and the glory, for ever and ever

When Freemasons say the Lord's prayer we use debtors. Which was the first time I had heard it done that way. I thought that we (Freemasons) were wrong until I researched and found out that it's very plausible that debtors is the correct translation.

My research showed that John Wycliffe in 1382, debts and debtors was used. Only the Tyndale version of 1525 used trespasses. I was completely perplexed! Ultimately we probably mean something like:

Forgive us our sins as we forgive those who sin against us.

But change is not something we do well :)

In line with what Mark Trapp said, please see this

This is an English translation issue, not a Protestant/Catholic issue.

Latin is the official language of the Catholic Church and the Latin says:

Panem nostrum quotidianum da nobis hodie, et dimitte nobis debita nostra sicut et nos dimittimus debitoribus nostris