Farm Stands are a great place to buy fresh produce. The price is generally lower than the supermarket because there's no "middleman" and you get fresher, better quality veggies and fruits. In many areas this is a seasonal thing so enjoy it while you can!
In some areas you can "pick your own" for greater savings. In our area there are places to pick strawberries, blueberries and apples. These fruits are labor intensive (especially the blueberries!) to pick so the farm passes on the savings to you.
Farmer's markets are also good. The local farmers pick their produce the morning of the market so you know it is really fresh. Since it is coming directly from the farm to you the "middle man" is cut out so you get better prices.
In 2004 we discovered and participated in the CSA concept. CSA stands for "Community Supported Agriculture". You buy a share of the crop by paying in advance then every week from June through the end of October (we live in Massachusetts so that's about it for the growing season) you go to the farm and pick up your farm fresh veggies. We paid $400 for our membership which came out to about $18/week. Over the course of the season we received 36 heads of assorted lettuce, 13 bags of "salad mix", 16 lbs of spinach, 21 bunches of Swiss chard, 13 bunches of radishes, 17 bunches of arugula, 6 heads of bok choy, 8 bunches of red and golden beets, 2 quarts of strawberries, 7 lbs. of assorted peas, 7 heads of cauliflower, 12 bunches of broccoli, 9 heads of cabbage, 19 lbs. of summer squashes, 10 lbs of beans, 20 cucumbers, 30 sweet peppers, 33 lbs. of tomatoes, 12 pints of cherry tomatoes, 7 dozen ears of corn, 15 lbs. of potatoes, 16 winter squashes, 10 bunches of carrots, and smaller amounts of onions, garlic, kale, napa cabbage, watermelons, cantaloupes, radiccio, celery, eggplant, leeks, brussels sprouts, hot peppers, fennel and an interesting vegetable called Romanesco. As of this update (2010) we are still participating!
In addition to the vegetables we got a fresh bouquet of flowers every week, fresh herbs (parsley, basil, dill, rosemary), and in the fall a large pumpkin, 2 bunches of Indian Corn and 6 gourds for decorating. Below is a photograph of one week's veggies.
We go to Intervale Farm in Westhampton, MA but there are lots of others around. Google "CSA" or "Community Supported Agriculture" with the name of your state and you will very likely find one near you.