I can't see any room for the Christian God in the Buddhist cosmology. In terms of traditional pagan deities, they are considered a class of beings which, while being very powerful and living extremely long lives, are still mortal and bound to the wheel of samsara like everyone else. On a more absolute level, there are Buddhist concepts like tathagatagharba or "Buddha-nature", which express some universal reality or ground of being, but these are too abstract and impersonal to be anything like our God.
While Jetavan is right that the Buddha never made a critique specifically of an all-powerful God who voluntarily limits his power to permit free-will, he did reject any idea of an abiding "self," in anything. While this is most usually applied to the concept of an immortal soul, it is also directed at the divine absolute "atman" and could just as well be applied to any personal deity.
A personal deity, in Buddhism, would be a being with a spiritual body, existing in a spiritual realm (a heaven, for instance), a being who has intention, desires, and motives. The idea of 'not-self' does not deny that such persons, or beings, exist, whether in spiritual realms or in physical realms (like this Earth).
What 'not-self' critiques is the possibility of pointing to any "thing" that exists without change, without mutability, without impermanence. Clearly, "I" still exist, even if the 'not-self' idea is accurate, because "I" am a body (that changes, that is impermanent) and a mind (that also changes and is impermanent).
If there is any "thing" -- that is, any thing that one can empirically sense, or any idea, feeling, though, concept, percept in one's mental state -- that does not change, or that is permanent, then the existence of such a "thing" would refute the 'not-self' idea and fatally undermine Buddhism. But I have yet to see any such a "thing".
Now, if one defines "God" as that which is "not a thing", then such a "God" lies outside the definition of 'not-self', and "God" would not be the object of the 'not-self' critique. Of course, the problem with talking about "no-things", like "God", is that people begin to argue that their idea of "no-thing" is superior to another person's, and since there is no empirical way to judge the accuracy of one person's idea of "no-thing", these arguments lead to "no-where".
This does not mean that "no-thing" does not exist. Indeed, Nirvana is the one "no-thing" in Buddhism, but you don't realize Nirvana by talking about it. Nirvana is realized by means of one's spiritual practice, centered on "things" one can empirically sense (e.g., matter) or mentally conceive (thoughts, feelings, intentions -- like love, compassion, wisdom, etc.).