No, Occam's Razor is not an especially priviliged principle and going for the simplest explanation of something is not, as the distinguished thinker Sherlock Holmes knew well, always the best.

Religious people sometimes tend to argue anyway that God's existence represents the simplest explanation of the phenomena. In that case, Occam's Razor would represent an excellent reason for being a believer.

Yes, "Occam's Razor" is just as relevant and just as appropriately applicable when deciding whether or not to believe in a divine being as in any other domain of rational enquiry. Why shouldn't it be?

But the principle is a qualified one: it only tells us not to multiply entities beyond necessity (it doesn't say "don't multiply entities", full stop). Applied to the case of religious beliefs, it says: don't postulate djinns or dryads, cherubim or archangels, or fully-fledged gods, unless there is strong reason to do so. But of course, some believers in God (as traditionally conceived) think there are strong reasons for postulating the existence of such a being. And in so far as they think that they ought to have such reasons, they are still conforming their belief-formation to the principle encapsulated in Occam's Razor (but, contra the previous response, I wouldn't say that Occam's Razor is itself a reason for their theistic belief -- their reasons are e.g. an argument from design or whatever).

I agree with Oliver that Occam's razor is not an "especially priviliged" principle in this or other contexts, but I also agree with Peter that it nonetheless is perfectly appopriate to use this principle when thinking about whether God exists.

Whether or not you will ultimately find Occam's razor useful depends, first, on your own intellectual aims and, second, your other thoughts about God. On the one hand, I agree with my colleagues that there is no prospect that Occam's razor can provide you with a "knock down argument" against theism: if such arguments exists, identifying and assessing them will require must more than an application of that single principle. So, if that is your intellectual aim I think you won't find much comfort in Occam. On the other hand, if you are interested in sustained philosophical reflection on whether or not God exists whether or not Occam's razor is useful to you will depend on exactly how your reflections go -- like any other component of one's "philosophical toolkit," this principle may or may not end up helping you to make intellectual progress.