Apparently the assertion that Christians and Muslims worship the same God is extremely controversial. I am going to take another stab at it to try to defend this position.
First, Christians and Muslims clearly have radically different conceptions of who God is, e.g. Christians are trinitarians; Muslims are unitarians. I am not at all attempting to refute this. Many would argue that the character of the Christian and Muslim concepts of God are also radically different, and I would tend to agree.
Second, Allah is synonymous with God. The former is the Arabic term for the latter. When the Bible is translated into Arabic, Allah is used in the same places where our English translations say God. Asking whether Allah is the same as God is the same as asking whether Dios (Spanish) is the same as God.
Third, there are two fundamentally different ways to think about identifying God. The first is to take God as the subject and then describe who God is. If Christians and Muslims provide contrary descriptions of God, it seems likely they are describing different gods. This is analagous to two people describing their friend Andy, who discover that they have been talking about two different people all along. On the other hand, we can take God's actions (specifically His act of creation) as the predicate and then attempt to discover who performed the action. This is analagous to two people calling their American Family Insurance rep and discovering that they have diffent conceptions of who he is.
It follows then that the theological models of who God is (as subject) are different. In worship, however, we are both addressing the Creator (as predicate). When we address our worship to the Creator, it is the creator who receives our worship regardless of who we conceive Him to be.