Historical precedents have shown that whenever the people have a means of obtaining items of currency (effectively) out of the ground, that governments will step in and not only demand a piece of the action, but will eventually shut it down. For example, the US government eventually made it illegal to use gold as currency, despite the gold rush that added so much to the country's wealth. The same may well happen with Bitcoin, as governments become nervous of a currency being created that is beyond their control, regulation may be imposed to prevent Bitcoin mining.
When Bitcoin began, it was easy to solve the cryptographic problems involved, so much so that CPU mining was practical. As the difficulty of these problems grew, the computation was handed off to graphical cards (i.e. GPUs) which are better suited to the type of calculations involved. At this point, Bitcoins were still being created with domestic hardware – even if it was the type of hardware that a hardcore gamer would own.
At the time or writing, we find ourselves with roughly half of all bitcoins having been mined. The difficulty the cryptographic calculations have created the need for application specific integrated chips (ASICs). These are digital form of heavy duty mining equipment, and is what will drive on the creation of bitcoins. If governments seek to take over, the otherwise anonymous, production of bitcoins then we may well see ASICs made illegal, or at least only available under expensive licencing.
There would be a degree of folly in this, though, as it is still possible for members of the public to mine bitcoins with their gaming rigs, and more importantly, band together in secret pools to combine their resources. Furthermore, limiting voluntary mining of bitcoins is short-sighted as there will always be other countries who will not outlaw such creation of wealth, those countries could then take over the production of bitcoins. Those may well be the same countries that western capitalist governments would be concerned about who would be making use of bitcoins.
In short, Pandora's Box has already been opened, and regulating won't reverse the situation. Just as with the DMCA in the US, regulation would end up hurting people who have no malicious intent, and doing nothing to stop those who are up to no good.
Because Bitcoin allows for identity free transactions, it is understandably of concern to law enforcement, and of course there is value in having an identity attached to financial transactions; e.g. for accountability and reversibility, and so identity-dependant financial systems are not going to be replaced any time soon. However, even in the face established digital payment systems (e.g. credit cards and online banking), tangible cash has not gone away either, and I expect ordinary people will eventually find equivalent online uses for digital cash – e.g. Bitcoin.