The race to the bottom effect has pretty consistently failed to happen.
While in general 'race to the bottom' (RTTB) refers to any loosening of regulations to attract foreign investment, these days when we talk about RTTB we usually mean loosening of environmental regulations. The theory is that corporations in rich countries will move their polluting factories to the countries (usually poor countries) with looser environmental regulations. This is sometimes referred to as the 'pollution haven' effect. But this doesn't actually happen on a large scale, and the economic benefits to poorer countries usually outweigh the costs (environmentally or otherwise) of foreign investments.
There are many different explanations as to why RTTB isn't happening. It may be because no company would want to build an expensive factory in a country so corrupt (and therefore unstable) that its government would trade off the well-being of its citizens for a little more money. And, older polluting technologies just aren't as productive as newer technologies that are initially developed in first world countries with tighter environmental controls. It could be that the pro-environment binge that the world has been on for the last 20 years has convinced all responsible nations to have at least rudimentary anti-pollution laws -- and made consumers hyper-sensitive to reports of pollution, making corporations keep it clean. And, generally speaking, the costs that the corporations are most worried about are the costs of labor, not the costs of anti-pollution measures.
All of these help avert the disaster of RTTB, and no doubt other factors contribute as well. Whatever the reasons, empirical studies have shown that pollution and foreign investment are not directly related. (Although in many cases, they are inversely correlated -- such as in China, Brazil, and Mexico). Furthermore, World Bank funded studies have found that countries with policies that are more open to foreign investment tended to adopt less polluting technologies faster than those with closed policies. Foreign investment is actually a great way to become exposed to new technologies and new ideas, and to gain the funds to implement these new influences.
An interesting analogy is the "California Effect". Since the 1970s, California has been leading the United States in tightening environmental regulations. But this hasn't caused industries to flee from California to other states. It has actually caused manufactures in other states to raise their standards to meet California's requirements, and has caused other states to tighten their own environmental standards -- a 'race to the top', albeit a very slow one.
Hong Kong is currently having a problem keeping the air of its cities clean enough to continue to attract foreign investment. The major polluters are foreign owned companies -- specifically, Chinese factories located in the nearby Guangdong Province of China. While Hong Kong doesn't have a lot of influence over China's factories, it will be working to reduce the second greatest source of pollution, its own power companies. Due to the benefits of attracting foreign investments, Hong Kong will be trying to move to cleaner, less polluting energy sources. (Probably nuclear power, a mixed blessing at best, but it will reduce air pollution).
Perhaps more directly relevant to the average noder, most companies don't even think about going to third world countries. Most foreign investments come from one first or second world country and go to another first or second world country. America, China, Japan, the countries of the European Union, Canada, Australia, and the other major economic powers prefer to trade with each other. Tim Harford reports that foreign investment in rich countries are more likely to be in polluting industries than foreign investment in poor countries, and that polluting industries are the fastest growing segment of foreign investment in the USA. Clearly, we have more to fear from foreign investment than does Cameroon.
Just because RTTB isn't destroying the world doesn't mean that globalization doesn't have its downsides -- but as RTTB, sweatshops, and reduction of trade barriers start to fade as economic bogeymen, we can start to look to the real problems -- loss of traditional cultures and ways of life, and the undeniable fact that the Earth cannot support over 6 billion people using resources at the rate that citizens of rich nations have become accustomed to.
Javorcik, Beata Smarzynska and Wei, Shang-Jin (2004) "Pollution Havens and Foreign Direct Investment: Dirty Secret or Popular Myth?," Contributions to Economic Analysis & Policy: Vol. 3 : Iss. 2, Article 8.
Wheeler, David, "Racing to the Bottom? Foreign Investment and Air Pollution in Developing Countries" (November 30, 1999). World Bank Policy Research Working Paper No. 2524
The Undercover Economist, Tim Harford, Random House, 2005