The population problem in many third world countries (in Africa, anyway; don't know about other continents) is twofold: firstly, a woman is primarily valued based on her childbearing ability, a cultural problem. The status of a man is determined by how many children his wife has (!!), so this leads to a number of problems. Second, education and literacy in these countries is very low, especially among women, so they have no means of making a living, therefore being subject to their husbands' whims and not having the resources or knowledge to use birth control.
(I'm not trying to stereotype here; I am saying these things based on a lot of things I've read and also an anthropology course I took. Bear in mind that these things are not true of all women in third world countries or in Africa, but conditions like this do persist in many cultures and regions.)
Not all women want to have children, and surely many third world women would like to have less or none.
What the world's governments should be doing, instead of giving handouts of food, is setting up educational programs and clinics in third world countries. This would (hopefully) help women to be more independent and to have control over their reproduction and family life.
Culture reform is another thing altogether. I don't agree with messing with someone else's culture, but if a culture is focused on how many kids a woman can pop out, and that causes a population crisis and consequent horrid quality of life...women need to be more empowered in these places, and people need to be valued not on their families but on other things. Perhaps this is where the education bit can come in: educating people that too many humans on too little land makes for wretched living conditions for everyone; that having a smaller family makes it much easier to save some resources so you're okay during times of famine. Perhaps they can educate them into a way of life that is more based on cooperation than competition.
I don't agree with randomly going out and sterilizing a bunch of people. I strongly feel that with proper education of all those people, many of them would make the decision all by themselves to be childfree or to have very few children. Note that this has happened all by itself in most of the "first world" countries (much of europe, japan, et cetera), due to proper education of both genders.
With education, one understands that one's worth amounts to more than kids.
With education, one understands that family planning can make the quality of life higher for everyone in an area due to freeing up resources.
Also, as a side note: the situation in China isn't as black-and-white as all girls being aborted and people automatically being sterilized after two children. There are a number of systems in place, including benefits for very small families (1 child), heavier taxes for larger families, and some rule-bending in rural areas where bigger families are needed for farming. I think sterilization is strongly encouraged for people who have had 2 children, but I don't think it's forced on anyone. I just get concerned about this because I know a very nice Chinese family from a girl I went to high school with...she was born in China, while all of this was going on. Her parents kept her and moved to the U.S., and went on to have another girl. Not all Chinese value boys more than girls, and not all of them would agree with something like abortion or infanticide.
The stereotyping when it comes to the Chinese really concerns me, because from what I've seen, they're a really great culture. They've produced some of the world's finest philosophers and arts, so I wouldn't sum China up as female infantacide and sterilization. Sadly, some people do, and that's what ticks me off. I'm not mad at anyone here in this forum, I'm just mainly mad at some of my fellow Americans who wallow in ignorance of other cultures and perpetuate icky sterotypes.
Anyway, yeah, looking at conditions in third world countries sure makes sterilization look like a lot less of a sin and a lot more of a blessing.