The main issue with the Grey Goo scenario is, as others have stated, energy. When you get right down to basics, self-replicating machines are basically just a new kind of life form, and will be under the same pressures to survive as any other living organism. You can't turn the entire planet's mass into robots without running into problems with energy sources and waste heat, so you're going to have to lower your ambitions somewhat to wiping out all organic life, turning the surface of the planet into one big solar power plant, and turning the crust into a network of geothermal power plants, with maybe some supercomputers in between. Still, an admirable goal for an aspiring mad scientist.
If you want your nanobots to take over the world, you need to build a better life form. So the question is, can human technology one-up billions of years of evolution and outcompete all life?
But all hope(?) is not lost! There are a few areas where engineers can put Mother Nature in her place, and one of those is, interestingly enough, energy. Photosynthesis is not actually all it's cracked up to be - it's good enough for life, but solar panels are about 10 times better at converting solar energy into usable power.
Evolution, for all its competitive spirit, tends to be more focused on survival and reproduction than killing. Sure, organisms kill each other all the time, but they do so because it enables them to reproduce, they don't reproduce in order to kill. Since you're engineering the goals and prime directive of this new form of life, you can give it different priorities, and most life will not be able to adapt fast enough to oppose them.
Also, you can let your machines build a computer to control their global takeover strategy, which most living organisms cannot do. Program it with your ultimate goal so that it can continue working on your objective once it has eaten you.
Unfortunately, nanobots can't construct things that fast, so destroying the world by next Tuesday is out of the question. And sooner or later pesky environmentalists and any other people who would rather the Earth not be destroyed will start to fight back. Now you're just dealing with a robot war. You can probably win that, though, provided you've planned ahead well enough.
You'll probably want to start your takeover of Earth in a place like the Sahara where silicon and sun are easy to come by. Start with self-replicating solar panels and turn the desert into your starter power source. The best part is, you don't have to give away your true intentions at this point - exploiting the desert's solar energy is a wonderful goal, and you can probably get world governments supporting you before you reveal your true intentions.
You can divert some of that energy to drilling into the Earth for geothermal power. More free energy...and more space to hide your growing robot army.
Once you have set your forces in place, it's time to reveal your hand. Now all you need to do is make more desert, and that's easy - we've been doing it for years without even trying. Slash and burn your way to victory!
Once you've converted the surface of the planet into one big solar factory and turned the inside into a network of geothermal plants, you're pretty close to exploiting all of the Earth's energy resources to their maximum potential.