Like many things, we want GMO decisions to be simple, but they are complex. Like what's been said, Monsanto, with mainly the herbicide roundup, has inserted a roundup ready gene into field corn and soybeans. Genetic modification. It has been very successful. Since weeds are one of the biggest problems for farmers, it makes management much easier. Plant the corn, wait till the corn and weeds have emerged, spray it all and only the weeds die. Science. But now there are beginning to be roundup resistant escapees. And, like EV said, we have been genetically modifying plants for years, even when we save a favorite variety's seeds, or only plant the seeds from the biggest tomatoes.
There is roundup ready sweet corn technology available but the public is worried. Another GMO - the BT gene, has also been inserted into corn. Bacillus thuringiensis - it is a biological pesticide "created" by Bayer that prevents worm damage. http://en.wikipedia.org/wiki/Bacillus_thuringiensis
We talk about organics. The organic issue is a bit like people wanting more government services and lower taxes. The public wants organically grown produce but no trace of insects, rots, or molds. We need to get used to blemished produce, and insects we need to wipe off the strawberries. Or, perish the thought, not abhor biting into an apple and seeing the other half of the worm.
There is also the organic fertilizer industry where companies spring up that spray all kinds of seaweed and brews - some may work, some doesn't. To the plant, it is nitrogen, phosphorus, and potassium that helps - it doesn't matter to the plant if it is broken up with a sledge hammer and horses or if it comes out of a bag. There are petroleum use issues, however, in commercial fertilizer production. Which brings me to another modification in agriculture. If you google the town of Almería Spain, here is the satellite picture of 20,000 Hectares of plastic in use to make it the greenhouse of Europe.
Like most things, we need to test and test and doubt and question and hold government and private industry's collective feet to the fire to make sure we are getting a balance we can live with. Remember DDT had full backing of universities, and only now are the bald eagles coming back.