Peace Everyone,
This has been quite an interesting thread--and for the most part, fairly free of animosity (quite refreshing!).
If we (monotheists) believe the One God to be a reality, then speaking of worshipping the "same" or a "different" single God is a bit odd. A monotheist believes that there is but ONE God, and any other "gods" either do not exist, or are not "gods" but rather created beings.
I think it is clear, on the theological level, the conception of God among Jews, Christians and Muslims has some similarities, but also important differences. For example, the Christian concept of Trinity is vastly different than the Muslim conception of the Uni-personality of God.
The question of "worshipping" the same God--this is problematic. Some (Christians) might argue that if you've heard of Jesus but don't think of Jesus and the Tri-unity of God in worship, then you aren't worshipping the One, True God. Others (Muslims) might feel exactly the opposite--if you conceive of Jesus as in any way divine, you are associating partners with the One, True God and therefore not truly worshipping God.
Christian Scripture is fairly clear (if you accept it), that one cannot have the Father who does not have the Son (see John 5:23, 1 John 2:23), and if you deny that Jesus is the Messiah you are a "liar" and "antichrist" (1 John 2:22). Therefore, I cannot see how a Christian (who believes in the inerrancy of Scripture--not all Christians do so) can believe that either Jews or Muslims are honoring God, in that they reject the Son of God. (Yes, I know that Muslims accept that Jesus was the Messiah, but not the 'Son of God', which they explicitly reject. Jews reject both Jesus' Messiahship and his Sonship.)
From John's writings, I conclude that a biblical Christian cannot accept that either the Jew or the Muslim (or anyone else, for that matter) who does not acknowledge Jesus' Messiahship and Sonship can honor God. And what is "worship" if it does not include honoring God?
Likewise, I believe that the Quran is equally clear (from what I have read in translation), that if one ascribes partners with God (which Muslims believe the Trinity would suggest), he or she isn't truly honoring God. (Muslims, if you disagree, please clarify.)
Now, I have to admit that I have problems with this view, though I cannot escape that this is what the New Testament or Quran teaches (though I acknowledge that I'm no Quranic scholar, and I could be wrong about that.) This is also why I feel that it is not exactly biblical for Christians to on the one hand believe in the inerrancy of the New Testament but on the other hand to believe that Jews who reject the Son somehow honor the Father.
All of this being said, I don't see how our sharply different views of God should make us enemies of each other, or make dialogue impossible. To be sure, to hear from someone "you're not honoring God!" is probably not the most diplomatic thing, and it is natural for us to get defensive. However, I think that rather than soft-pedaling the teachings of a religion, we should be open and honest with each other about what we believe (or at least honest about what religious texts state, even if we don't believe it.)
Peace,
Daniel