We already have way more than enough food to feed the entire world. As it is huge amounts of food go to waste every year. The problem is not that there is not enough, but that the people in countries cannot afford it, and if their harvest fails they can't afford to have it imported either.

Ah, so why don't we give them this food that's going to waste for free, we have no other use for it? Well, that would bankrupt the economies of the countries receiving the food. In those places many peoples livelihoods rely on the food industry; farming is the one of the most common occupations, and then people get employed to package, sell, collect or prepare the food the farmers grow.
Now imagine what would happen if suddenly there was loads of free food around. Why would people still BUY the produce grown in the country? They wouldn't. As no one was buying he food the farmers would go bankrupt as they would make no money. As the food industry would make no money, and thus collapse, the other people payed to package, sell, collect, prepare, etc the food grown wouldn't make any money either, as they would be out of a job or their employers couldn't afford to pay them. Many, many people who previously had a job and enough money to survive would be much, much poorer. This would be especially bad considering in most third world countries the food industry is the main employer.

Thus giving third world countries free food would make the people even poorer.

Also it'd screw up the rest of the country too as the food industries are very important to the economy.

The world does in fact produce enough to feed everyone. Double actually, according to the Food and Agriculture Organization of the United Nations. The problem lies in distribution, which is inadequate to feed everyone as it is now.

The world does produce enough food for everyone, the problem is distribution.
However, by 2025 this may not be true. Food production will have to double.

http://www.infoforhealth.org/pr/m13/m13chap1_2.shtml

Currently enough food is produced to feed the world's population. Otherwise you would be reading of mass starvation in poor countries.

There are problems of distribution in parts of the world that are undergoing civil wars or similar disruptions. The richer nations and their charities attempt to send food to any area with starving people; but, it can't be done successfully where there is warfare going on or violent anarchy (such as in Somalia).

In the near future the world will be unable to feed everyone because the population is growing faster than any possible increase in food production. Few countries have been willing to attempt to stabilize their populations, mostly because of misguided religious and economic beliefs. The result will be mass starvation and/or associated deadly epidemics (people resist disease less strongly when undernourished).