Globalization vs. nation-states is indeed a false choice, as others have said. We have already seen the rise of multi-national corporations, trans-national terrorist organizations, and I anticipate more challenges to traditional notions of the state, which really has only existed in its current form for less than three centuries, in the future.
I think that while globalization does have the effect of spreading ideas and products globally, there is more to "state" than just economics. Culture is deeply rooted, and doesn't change as easily as other areas of life, so I expect that while the world may grow more "flat" as Thomas Friedman put it, it will never be singular.
Globalization is not a threat to the state, obviously, since the economic process f lowering bariers to trade and production is well underway and even complete or in second and third stages in some countries, yet the system of world government is largely intact.
To a lesser degree, I think the recent "Arab Spring" revolts in North Africa and the Middle East have an indirect tie to globalization, and the freer exchange of ideas and goods and services, as well as internet and phone access being cheap and plentiful, which has made revolts easier to organize and coordinate.
It's possible to argue that globalization has already resulted in a growth of freedom in general. As ideas about democracy have become more and more widespread, democracies have become more common. As technology has brought more and more people around the globe into touch with one another, countries have found it harder and harder to prevent democratic developments. This is one reason that tight restrictions are placed on the internet in totalitarian countries. I recently had some great students from China, but we cannot stay in touch with each other through Facebook, since Facebook is banned in China.
The question is put into a false binary. Globalism will benefit many countries and it will hurt many others. Usually nothing is completely beneficial or negative. I can see globalization helping nations with money and power, since they usually have the ability to make agreements that benefit them. Nations that are weaker will continue be exploited. This seems to be the pattern of the world.
#2 has accurately captured one aspect of how globalization has been affecting people.
But it is worth considering the fact that people usually tend to look for what is the more familiar and closer when the new and unexplored tends to pose a threat. If globalization were to bring something beneficial to everyone it could lead to the slow dissolution of boundaries and ultimately end formal nationalism. There would be the formation of larger states allowing a free movement of goods and labor across borders without any restrictions.
I don't think there's enough evidence to make any real confident predictions at this time. My gut feeling is that globalization, particularly as supported by the technological changes that have made communications immediate and easily accessible to anyone with the right connection, will result in changes in the role of separate states/countries, but I don't think that concept will vanish.
It seems unlikely that globalization will destroy the state. In the past, it was said that globalization would destroy nationalism, but that has not happened. It appears that people need to feel a connection to what is close to them. It is likely that an increase in globalization will make people retreat even more into what is close and familiar, and that will be the state.