It depends on what god you mean... I will share with you what I know (or think I know XD)...
My God, the Christian God, does not REQUIRE worship to survive or have power, or at least, that's what I have been told. Admittedly, I have not seen God when absolutely no one was worshipping (no matter how beaten up Christianity and Judaism got, there were still a few...). I suppose, though, that since he had the power to create the world before there was anything to worship him, he does not NEED worship. (Or was there things to worship him? Did God create other solar systems, galaxies, universes, and dimensions before creating our own? Hmm, maybe God started out with single celled creatures, and he got more power from their worship, and then he progressed to more advanced single celled creatures, and eventually to small multicellular creatures, gradually getting more advanced, eventually getting to the dinosaurs and such... after soaking up enough power from their worship, he decided he was ready to go further. However, first he had to get rid of the dinosours. Fortunately, being omniscient, he planned this out in advance - the sun was scheduled to undergo a major change in size, I think from white dwarf to yellow thingy [don't remember all the names and such XD], killing off most of his previous work. Then he proceeded to create the world as we know it in quick time, giving rise to our 7 day creation story =D. Also, since he knew he would be working with sentient beings, he made it so that inanimate objects like the rocks could worship him in case the humans ever stopped, effectively giving him unlimited power, and thus he was telling the truth when he said he was omnipotent [er, now that I think about it, did he ever say that he was omnipotent?]. Sound good? No, no, wait, that would never work, the first sentence [or was it second?] in the Bible states that the earth was a formless mass... maybe the sun melted the earth before God started working with it again?)
However, if you are refering to the pagan gods, Vishnu, Zeus, Ra, Thor, and the like, yeh, I think they need worship to have power. I personally believe that they come about entirely from human imagination - not saying that they aren't real by a long shot, I'm saying that the process of being thought up, visualized and worships brings the entity into this reality. So yes, "false gods" are real (I'm probably the only Christian who will tell you that XD). I think that's why God said only to worship him - I mean think about it, if you were God, would you want to have to deal with a bunch of other gods that are gaining power from what YOU created?
Of course, the whole idea of false gods being demons or men sponsored by Satan works too... XD