The original Greek of the text in the gospel of Matthew does not say "do not let us fall into temptation" but "do not lead us into temptation". It is not the same thing, and to change the translation in this manner is not true to the text; this is more than a paraphrased interpretation, but an actual change in the meaning. In other words: not good, and not faithful to the biblical text. Another one of the problems we encounter with this twisting of the passage is that the Greek word for "temptation" has just as much a connotation of "trial" as it does "temptation" (because trials are a temptation to sin, and temptations are always a trial--the difference is in context).
Let me add one more layer to this entire situation that I have not heard anyone else refer to. There is another text in the Scriptures that specifically says that God does lead into temptation (at least once). Yes, I know that sounds crazy; I also do not pretend that I can perfectly interpret what that means, but the Scriptures say it so we cannot deny it. Here is the passage I speak of:
Then Jesus was led up by the Spirit into the wilderness to be tempted by the devil (Matthew 4:1).He was led "by the Spirit" "to be tempted". In other words, Jesus was "led into temptation" by the Holy Spirit Himself. Again, I am not saying I can perfectly understand how this works, but we can all be confident that whatever the Holy Spirit did it was not a sin. In the gospel of Luke it also says He was "led by the Spirit" and in Mark it says the Spirit "drove" Him there. There is no doubt about it (and we all know it) that Jesus was specifically sent there to be tempted. If it was not wrong to say that God did it to Jesus, how could it be wrong for Him to do it to us?
Let me add another Scriptural detail here. In the book of Deuteronomy, the Lord tells the Hebrews that, after delivering them from Egypt, He led them into the wilderness and sent them through trials to "test" them (Deut 8:16; and there are many other passages of similar reference). Thus, the Lord intentionally put them through certain experiences of difficulty and trial so that He could test whether their faith was genuine. This does not surprise anyone who is familiar with biblical history.
What does this mean for us in this question of the translation of the Lord's Prayer? At the barest minimum it means that there is nothing wrong with saying "lead us not into temptation" and it should not give anyone the wrong idea. We know that God Himself does not tempt us to sin (the original wording of the Lord's Prayer does not say that He does!). The Lord's Prayer asks that He not "lead us" into a place where there is temptation (i.e. trials, testing, etc.). Just as we pray that He will deliver us from evil--and yet we know that at times He chooses not to do so--also we are to pray that He not lead us into that same kind of trial and temptation like Jesus experienced (even though we know that He may choose to do so in order to test our faith like He did with the ancient Hebrews, or even with Job).
In the end, however, we must ask: does it make a difference? We are asking not to be tempted (however we attribute the causality). I think it does make a difference and that there are two very important things at stake here. First, the desire to change the wording of the prayer to the phrase "do not let us fall into temptation" reveals a fundamental misunderstanding of what temptation is all about. Being tempted is, of course, never a good thing (in itself), but it is a trial and testing of our faith that (when we overcome it) is comparable to the strengthening of a bone after it heals from a break. We are able to stand firm afterward, like Jesus did after His temptation by the devil.
We are all going to be tempted to sin at various times because we are fallen beings who live in a fallen world (cf. Luke 17:1, "temptations to sin are sure to come"). Many of these temptations we are able to overcome by the power of the Spirit of God. When, however, we encounter a situation that is a much more serious trial and temptation we are called to remember that God is still present and able to help us. No, we do not want to go through that trial, but when that prayer that He "lead us not" is not answered, then we are still supposed to turn to Him Who is always with us "unto the end of the age".
This is the second thing at stake. In removing the reference to "leading us" into temptation (which echoes the temptation of Jesus) we are also removing the point that God is involved in every aspect of our lives, even when we endure great trials and are tempted to sin. Asking God not to "lead us" is acknowledging that our temptations that each of us experience are not mere happenstance events, but are actually a part of God's oversight in our lives. He is there when we are tempted, and sometimes He brings us into that situation precisely because He wants to test our faith, have us pass the test, and then be stronger as a result.
This does not mean He does the tempting with us (any more than He was the one who tempted Jesus in the wilderness), but it does mean that all of our spiritual struggles are a part of our relationship with Him. All He has to do in this is place us in a situation where He knows temptation will occur, and if He does it, then we know it is for our good as much as it was for Christ's good. If we merely petition God not to "let us fall" into temptation, then it makes it seem as though He is just a passive observer Who is being asked to step in when things get messed up in our lives. He is much more than that; our Lord is an active participant in everything we experience, and He is there to help us through it (as the Spirit was for Jesus--cf. Mark 1:13).
All in all, we can take hope in this one most important thing. Even though the world is filled with temptations, and we know that we will encounter them, and even though we are told to ask not to be led into temptation, yet you can always be confident that "God is faithful, and he will not let you be tempted beyond your strength" (1 Cor 10:13). This means that He does allow us to be tempted, but always makes sure to provide for us a means to overcome the temptation. So then, whether He is merely "allowing" us to be tempted or actually "leading" us into temptation, we can be sure that it is always for our good, and we can always go to Him to find the strength to endure.