According to Wikipedia, "grey goo" is a hypothetical end-of-the-world scenario involving molecular nanotechnology in which out-of-control self-replicating robots consume all matter on Earth while building more of themselves.
What many transhumanists and nanotechnology advocates forget is that simple earth-based bacteria and viruses also operate on identical principles to the hypothetical "grey goo". A bacterium converts nutrients and water from the environment into organic matter for reproduction. If a bacterium were to divide every hour, there would be enough bacteria to cover the entire surface of the Earth after just a week.
Of course, we know this doesn't happen because limiting factors will eventually slow down and stop the rate of reproduction. Similarly, in a "grey goo" scenario, the self-replicating nanobots would not continue replicating forever. Eventually, the raw matter needed for replication would be exhausted and the replication rate would be reduced to a crawl.
So why exactly do people continue to say that "grey goo" a threat to mankind?
Mainly because it is a sensationalist anti-nanotech propaganda piece, too often protrayed in fiction as a boogy man.
The Grey Goo Problem is one Drexler listed as a extreme, and extremely unlikely, danger in Engines of Creation due to his concerns that no-one would take the issue of developing safeguards for nanotech development seriously. And sadly, people like Richard Smalley, and Hollywood, continued to spread this idea to all listeners. Grey Goo is akin to making a car that can not only go out, chop down a tree, convert it to fuel, and use it to keep itself fueled while simultaniously mining the raw ores and other elements needed to make a copy of itself, processing them, and manufacturing it's identicle twin. It is TECHNICALLY feasible, but the levels of complexity needed are far beyond what would be required for manufacturing, even if self replicating systems are used. The simple solution even when dealing with self replicating systems is removal of the ability of a self replicator to fuel itself. So long as it had to exist in a solution of fuel and preprocessed materials, a far simpler task than making it self fueling and self processing, even self replicating systems could be easily contained.
There are legitimate uses for full self replicating machinery, particularly in space, where size and weight limitations make a good reason to allow self replicating machinery to exist, but here again, even making self replicating mining bots can be controlled with proper design. A self replicating miner could be sent to the asteroid belt and allowed to process the raw materials, but it need not be a nano machine. Small fist sized robots would work just as well. Similarly, terraforming bots would utilize nanofabrication internally, but also need not be nanoscopic themselves.
The majority of fears relating to Nano scale fabrication is due to a failure to comprehend what is actually involved, and fed by the same fears that hampers AI research, a fear that our machines will destroy us. In all cases, it is primarily due to lack of solid information and misconceptions. The only solution is education.