I've heard this idea thrown around a lot, but the only plausible explanation for such a phenomenon that I can come up with, is that all of the people on the internet suddenly act as a cohesive self. That is, like a person, people on the internet come to a decision and carry out that decision- just with a whole lot more brain power involved in the carrying out phase. The other possibility would be some conglomeration of search programs and other internet software and metasoftware become extremely widely distributed, and begin to feedback on each other in a powerful loop. There would be some very distinct necessary components to this that are fundamental to intelligence in order for this to work, and thus this is very unlikely in my opinion.
So, to an extent we can say that the internet is awake to a very small degree. Not so much really, but if people came to the realization that acting more like one self is incredibly more efficient than acting closer to like 50,000,000 selves, then perhaps...
So either way, this is pretty much an implausible scenario.