It's an very honorable idea they are pursuing, and I hope they succeed, but the rational part of me has always been very skeptical of their concept.
Here's what the realist side of me says:
If the countries are really really poor, then a computer is useless because all your time and energy goes towards trying to survive, they need clean water and vaccinations instead.
If a country is very poor, but not starving, then a computer is useless because they have no problems that a computer solves for them. the extent of their math needs ends at being able to keep track of the number of sheep in their flock and things like that. Not to even mention the fact that they don't have power to run computers anyway (the hand crank or other options are not feasible), they don't have affordable net access, etc., so a computer does them no good.
If the countries are poor, but not very poor, then they will have electricity and a reasonable net access price, and a growing opportunity for computing power to help them in their lives. However, a modernizing country isn't gonna want to have their new tech generation of kids learning an OS that by design is intentionally completely different than all the other OS's used in the countries around the world that they're trying to become like and do business with. Plus, at that point they are modernized enough that slow speed shipping to their area would be cheap, and it would be more helpful to them if we just shipped a boatload of our obsolete computers to them (which were otherwise just headed to the land fill) and train one local resident really well how to fix up old computers running linux.
I just don't see the population that would benefit from this computer.
Read more info on the OLPC project