First I think I should point out that many headlines state something along the lines of "Stephen Hawking says God did not create the universe". It's worth noting that this is not a direct quotation, and that what Hawking actually says is that given the law of gravity, one need not invoke God to explain the existence of the universe. This may be a small distinction but worth mentioning because it does not say that God certainly did not create, or that it is impossible that he created.
So what did he actually say? Direct quotations from the recent press release are:
"Because there is a law such as gravity, the universe can and will create itself from nothing. Spontaneous creation is the reason there is something rather than nothing, why the universe exists, why we exist,"
"It is not necessary to invoke God to light the blue touch paper and set the universe going."
"That makes the coincidences of our planetary conditions -- the single Sun, the lucky combination of Earth-Sun distance and solar mass, far less remarkable, and far less compelling evidence that the Earth was carefully designed just to please us human beings,"
The most pertinent one is the first, and I will be focusing on that one. My response will be on two levels. First pointing out that this particular model of the universe that he is referring to is one of numerous models of the universe, and the theoretical multiverse, none of which has been verified empirically. So there is nothing that compels us to accept the conclusions he draws from the model that he is in favor of since that model is not necessarily representative of reality, it is only one of various possibilities. Secondly, even if the model that he supports does in fact turn out to be a true representation of reality, then--even given what he says--God is still not necessarily ruled out. Neither is he made any less necessary.
Note the form that the first statement takes. "Because there is a law such as gravity" - the statement presupposes gravity as a brute fact, as a given, apparently without need for explanation. Why does the universe need an explanation but the law of gravity doesn't? Even if the law of gravity acting on 'nothingness' would inevitably result in the universe (again, which is something that is itself unsubstantiated), this only shifts the question from "where did the universe come from" to "where did the law of gravity come from?" A materialist conception of the universe will invariably run into the problem of an infinite regress until it comes to a true beginning or source beyond which no further inquiry can take place. Saying "because the law of gravity exists, the universe can and will create itself from nothing" is a bit like saying, 100(0)s of years ago when we learned how the Earth was formulated, "because the law of gravity exists, the Earth can and will create itself from nothing." Gravity certainly was instrumental in discovering how the Earth was formed, but it doesn't eliminate the need for further inquiry, but rather immediately poses a variety of other questions that need answering. And the same is true here. The law of gravity is not nothing, but something. This seems to be a very simple categorical or philosophical oversight by Hawking.
The third statement also deserves a brief response, but I'll defer to astrophysicist Hugh Ross who does a very good job of responding to this particular issue in a recent episode of the Science News Flash podcast. But, to paraphrase Ross, Hawking is just mistaken on this point, the evidence does not support what he is claiming.