After addressing the "Dirty Dozen," or foods you should buy organic, I decided to give some explanation as to how you can buy organic food without blowing your food budget.
In my own experience, I've found some good deals on organic fruits and vegetables at both Meijer and Kroger, including romaine hearts, grapes, strawberries, grape tomatoes and bananas. Just take a glance around your produce section.
I'd like to direct your attention to a few resources:
Staying Lean in Oakland County had a blog post on this very topic yesterday which I could not have researched or written better myself.
Shannon at For the Mommas has a good post about Buying Organic on a Budget (published about a year ago). It's full of great suggestions, such as checking out your local farmer's market and gives links to several companies that feature organic food and have coupons. I didn't check all of the links, but tested the first two, which worked.
Also, in 2008, the Grocery Coupon Guide did an exhaustive article about where to find organic and natural food coupons, that, although it's more than a couple of years old, is still a good general resource.
Many of the foods you buy, such as Pacific Natural Foods, or So Delicious Coconut Milk products by Turtle Mountain, have signups for their coupons. In the case of So Delicious, I was unable to sign up (probably due to my lovely dialup), so I sent the company an e-mail explaining I wanted coupons. They asked for my address, and I got them in the mail within a couple of weeks.