This is a good question, as people usually only speak of the positive elements of globalization. Therefore, to look at the downsides is wise. Here are a few downsides of globalization.
Arguably the greatest downside to globalization is that jobs are taken from industrialized countries and moved to places where labor is cheaper. The perfect example of this is America. Many factory jobs and manufacturing jobs are no longer here, as there has been a move to China and now even Southeast Asia. This move also creates resentment and in time the labor force in industrialized countries loses skills, such as in manufacturing. On the flip side, often workers in these poorer countries are forced to work in subpar environments. In short, they are exploited.
There are also environmental issues. Many third world countries or poorer countries use up their natural resources to feed the desires of wealthy countries. For example, many trees are cut down to provide cheap lumber to more advanced countries.