I asked myself this same question.
Organic milk can last up to a month, versus regular milk which lasts about a week. It has nothing to do with it being organic (cows are not treated with antibiotics or hormones) but rather how it is pasteurized.
Pastuerization= A method of treating food by heating it to a certain point to kill pathogenic (disease-causing) organisms but not harm the flavor or quality of the food.
Organic milk usually has to travel far from the farms to get the store shelves, so it is pasteurized using a process called UHT, Ultra- High Temperatures, where milk is heated to 280 degrees F for 2-4 seconds killing any bacteria present.
Most milk isn't heated to UHT because it may have a slight sweeter taste than regular milk, and some people just dont like that (I didn't mind or notice).
You may be getting a better milk product as well. Organically raised cows (who are usually grass-fed) produce milk with higher levels of antioxidants and fatty acids such as omega-3 fatty acids.
MY RECOMMENDATION!?
If you aren't a huge milk drinker and you find you always seem to have half full expired milk cartons in your fridge, go Organic and get a longer milk shelf-life! You will pay a bit more, but it certainly pays off!