Do genetically-modified foods have a negative effect on human health?

I’ve heard about African nations with food shortages turning down food aid packages that included genetically-modified rice. Cows in the US are fed genetically-modified corn because people don’t want to eat it.

I have to admit, I wonder myself if we know enough about manipulating fruit and vegetable genomes to prevent them from affecting our human physiology. DNA strands and genetic markers work in subtle ways we don’t yet understand; tweaking them might have effects that are not immediately clear.

Is it possible that messing with the DNA of food could have a negative effect on our own DNA? Is there any solid evidence concerning the safety of GM food?