For this one, we have to go to the cynical version of The Golden Rule: Those who have the gold are the ones who make the rules. In our modern society, those gold keepers are the corporations. They have the money and the resources to set the legislative agendas of many nations, passing laws to suit their needs. In this sense, the corporation is more powerful than the country.
These people, they're like ghosts, always hiding in the shadows, always hiding behind lies and proxy soldiers. A name won't mean much, they'll use whichever one suits their interests. Sometimes it's the Masons, sometimes the Bilderberg Group. They've had a finger in every corporation, organization, or government initiative that has defined modern society!
Corporations have top government officials on their payroll and the government policies are dictated by corporations. So even if we see government taking action, it is the corporations who ask the government to do so in the first place. Corporations do everything behind the scenes, be it lobbying for change of policies to benefit them or asking higher ranking officials to lobby with other country officials.
There are many reasons why I say yes, but I will only list two.
1. Money makes the world go round. Large corporations often are run by wealthy men and women. This is where the not outright comes into play. If you have a rich, charismatic, popular person, you can easily get them in a political seat, or fund someone who will get elected. People in power usually help the ones who help them get there.
2. Privatization. Security contracting and privatized space operations are already in place. For hundreds of years mercenaries have been used in warfare, but now large corporate entities are able to amass large armies of these private soldiers and equip them and sustain this without worry of public outrage for the erratic spending. Also with the new private satellites and space flights its not out of the question that their surveillance and communications would rival the governments. Many other aspects of life are privatized but are too numerous to list.
Countries rely on big corporations to help bring in local and international business, which in turn affects how countries operate. If corporations branch out they provide more jobs for he country they're in and inflate their financial status. Countries are at the mercy of corporations because the corporations have more power to make their surroundings thrive or die, whereas countries can't operate efficiently without the ongoing business that corporations bring.
First you have to define what power is. In many ways corporations are more powerful than many countries - they have more money and can use that weight to influence and lobby governments, however they still have to lobby those government to get their preferred laws through so ultimately the power lies in the states.
Also from a realist perspective - power comes from the barrel of a gun - until corporations have their own armed forces (which may happen on some level in the future) controlled violence still rests within the state system.
Another example against corporations being more powerful is China - they tightly control corporations and their activities in their country demonstrating that it is still possible for states to be more powerful. ~If a corporation influences policy it is because a state allows them to.
Some large corporations have gross profits that are more than the gross national worth of some small countries. Those corporations are really just big companies. The government of a country holds the power. A country may look to its largest corporations to help with employment and trade, but the government has the power to make the laws.
Just because corporations, and any associated downward financial spiral, that may trigger devastating effects for individual national and global economies, does not prove that these corporations are more powerful than those countries themselves. A corporation may be able to create an economic collapse, but to say that they can affect public policy, or directly control the government within the country, would certainly have shades of conspiracy theory written all over it. Corporations do present an ominous presence in our world, but to claim they are more powerful than any individual nation, might be met with swift and complete military résistance.
While I would definitely agree that corporations are indeed entities in the world that hold a lot of power, I don't think I would go so far as to say that they are more powerful than countries. They cannot have their own economy, or a standing army of anything of that sort.