Pollution is certainly one example of this. Another one that has been relatively well-publicized lately is the deforestation that has been happening in places like Indonesia because of the global demand for palm oil. This is an example of the environment being degraded in order to produce a good that is desired all over the world.
Palm oil is a commodity that is needed today for use in cooking, but also for biofuels and for use in cosmetics. Because of this, the price of palm oil has been rising. This makes people and countries want to grow palms for oil. In places like Indonesia, this has led to the destruction of natural forests. This has also led to an increase in emissions of greenhouse gasses. As the worldwatch.org link below says,
Due mostly to oil palm production, Indonesia emits more greenhouse gases than any country besides China and the United States.
There are many other examples like this. The basic idea is that a globalized economy can create increased demand for goods. Countries often start to degrade their environments in order to meet that increased demand.