In a worst-case scenario, all of the matter in the universe could be turned into goo (with "goo" meaning a large mass of replicating nanomachines lacking large-scale structure, which may or may not actually appear goo-like), killing the universe's residents. The disaster could result from an accidental mutation in a self-replicating nanomachine used for other purposes, or possibly from a deliberate doomsday device.
It is unclear whether nanotechnology is capable of creating grey goo at all. Among other common refutations, theorists suggest that the very size of nanoparticles inhibits them from moving very quickly. While the biological matter that composes life releases significant amounts of energy when oxidised, and other sources of energy such as sunlight are available, this energy might not be sufficient for the robots to out-compete existing organic life that already uses those resources, especially considering how much energy they will use for locomotion.
If the nanomachine is itself composed of organic molecules, then it might even find itself being preyed upon by preexisting bacteria and other natural life forms. One convenient analogy for the grey goo problem is to consider bacteria as the most perfect example of nanotechnology; as they have not reduced the world to grey goo in 4 billion years of evolution, it is unlikely that some artificial construct will manage to do so.
If they are built of inorganic compounds or make much use of elements that are not generally found in living matter, then they will need to use much of their metabolic output for fighting entropy as they purify (reduce sand to silicon, for instance) and synthesize the necessary building blocks. There would be little chemical energy available from inorganic matter such as rocks because, aside from a few exceptions (coal, for example) it's mostly well-oxidized and sitting in a free-energy minimum. Drexler has made a somewhat public effort to retract his hypothesis, in an effort to focus the debate on more realistic threats and misuses associated with knowledge-enabled nanoterrorism and other misuses.
Because of these limitations grey goo may only be possible in an environment which lacks indigenous life to compete with it for resources. However, some proponents of nanotechnology argue that artificial nanomachines might be able to outcompete natural life because they could have irreducibly complex designs that life could not have developed via natural evolution.
Recently, new analysis has shown that the danger of grey goo is far less likely than originally thought. However, other long-term major risks to society and the environment from nanotechnology have been identified.