Short Version
Provide no aid to Third World nations and you can expect widespread damage to the environment that will have a negative impact on all of us.
The Long Version
I've read through this thread and seen some statements to the effect that we should let Third World countries fend for themselves and let their populations 'stabilize' naturally. Bad idea for two simple reasons: the needless suffering that's created by this attitude and the destruction this attitude indirectly leads to. I won't bother to address the ethical side of the issue (some of you seem to think that ethics are a waste of time). Instead, I'd like to point out why it's practical to help out our poorer neighbours.
Ever heard of the slashing and burning of South American rainforests? The poaching of endangered species? Find it outrageous that people kill mountain gorillas to create ashtrays? If you aren't outraged by it, I'm sure that you can at least agree that the destruction of natural habitats and the reduction of biodiversity is a harmful practice - it creates imbalances in the ecosystem that all of us ultimately have to deal with.
At this point you might be thinking to yourself, "Those Third World pricks. How dare they destroy the environment." Well, quite simply, they dare because the impoverished farmer needs grazing land for his cattle and the poacher needs to feed his family. Since these nations are economically underdeveloped, and raw unfinished goods (e.g. agricultural) are their primary export, the outcome is pretty much predetermined.
That's the first reason I offer as to why we should be helping Third World countries to develop(For those of you who like to bitch and moan about 'handouts' what I'm proposing is that we teach the man to fish, not give him a supply of fish). By transforming the economies of third world countries to infrastructures based on skilled labour (as opposed to agricultural products), we can help to preserve the environment. As a general rule, people show more interest in preserving the environment when their survival isn't at stake.
Reason number two: I've already argued that population growth rates decline when a country reaches the post-industrial level of development. And a simple reason for keeping populations below the 'correction' threshold is the following: the fewer of us there are the better the earth can sustain the load.
In this day and age, there really is no room for regionalistic thinking. The fate of your fellow man is your fate too. Truthfully, the cost of helping Third World nations if far outweighed by the cost of not helping them.