Well, I am an "inclusive monotheist," so yes I believe we all believe in the same God. We all believe in the God of Abraham, so it seems rather obvious. But I personally would go even farther than that. For me, it is clear that there is only one God, or Divine, or whatever you want to call the Creative Force/Being that upholds the universe, that he/she/it is ultimately unified, although can be manifested in a variety of ways (such as the Shekineh in Judaism, or how we Jews say that every created thing has the spark of the Divine in it). For convention's sake I'll call him God. We cannot fathom this infinite God because we are only finite beings -- therefore we perceive only in part. This is why we have differing ideas about the Divine -- it's the old Buddhist tale of the blind men and the elephant. So IMHO whether we address the Divine as God, Jesus, Brahmen, Tao, or Lamed (I just made that up for this post! LOL) it doesn't matter. We are addressing the Divine as best we can, and he/she/it hears us.
Now, as to the more conventional explanations.
Judaism considers Muslims to be Righteous Gentiles, meaning they serve God and do good. On Christians, it depends what Jew you ask. (Christianity is always a sticky subject because of the long persecution that has only recently ended.) Some Jews say tht because Christians worship a man, Jesus, as God, that this cannot be the same God as the God of Abraham. But other Jews (including the Orthodox) do not agree. They say that a Gentile can have a symbol for God (such as the sun in Egyptian monotheism) and it is not the same thing as idolatry for them. Finally, Messianic Jews exist, let's just admit the reality, however uncomfortable it is for Jews--it makes no sense to say we can have Buddhist Jews and atheist Jews and Jews who believe the Rebbe is the Messiah, but if a Jew believes that Yeshua is the Messiah somehow he's not a Jew? A large minority of the younger generation of Jews accept MJ's as fellows Jews (accepting their beliefs is another issue).
Islam considers Christians and Jews to be "People of the Book." They were simply classified differently than polytheists. Again, it's going to depend on which Muslim you ask. Some say they are simply tolerated because they are monotheists. But others will say it is because they also worship the same God.
In Christianity, there is also a divide. Evangelicals tend to take an exclusive stance that because Jews and Muslims don't believe Jesus is God they worship a different God. But Mainline Churches and Catholicism look at things differently. Catholicism came out with a whole document during Vatican 2 that deals with its commonalities with Muslims and Jews. I think the whole point of Nostra Aetate is that when a Jew says he is praying to the God of his fathers, he actually is.
