When thinking about the future of the capitalist system, one quickly bounces against a puzzling paradox:
On one hand, there will be an inevitable push for private companies to take over certain responsibilities from governments (the 'market state'), a trend that is reinforced by the high levels of debt which will drag on countries' finances for decades to come.
On the other hand, we might see a push from the wider public for governments to take a more active part in parts of the economy that used to be private. This has happened recently with the banking sectors (states taking control over failing banks), but we might see this happening in other sectors as well, to avoid BP-like disasters for instance (caused by an ever increasing hunger for profit, which is would not necessarily be the case for public companies).
You might argue that government-run companies lack the drive to innovate, and hence this trend would stand in the way of human evolution. This should not necessarily be the case though: given the right stimuli to employees of state-owned companies could still stimulate innovation. A bigger hurdle is the fact that governments cannot be both the regulator and the regulated. However, in the case of financial institutions, this might turn out to be an advantage (at least governments would understand what they need to regulate).
It's going to be difficult to find a balance between both trends, but either way it will have a profound impact on our economies...