The article The Twenty Healthiest Foods for Under $1 from Divine Caroline has a list of healthy foods to help you eat healthy while saving money on your grocery budget. Imagine how much you could save if you grew them yourself.
Depending on the amount of land you have it may be difficult to grow enough oats for your use. Purchasing in bulk for storage would save you even more. If you are in an area that allows chickens you can produce your own eggs. Potatoes, kale, apples, and broccoli should not be much of a problem for most people. Apple trees can be purchased in a variety of sizes including columnar and dwarf to save space. Be sure to get two for pollination or you may not get a crop. Some variety of nuts can be grown in most climates. Depending on your climate you may or may not be able to grow bananas outdoors. Bananas can be grown as a houseplant - be sure to purchase a plant that produces edible bananas and be willing to wait about 18 months to harvest. Beans can also be grown in most climates and also store very well. Beans can also be sprouted for eating.
Of course if you are growing your own food you can save money growing a much wider variety than this. Add foods in a variety of colors to get the most range of nutrients - tomatoes, peppers, and berries are all colorful and fairly easy to grow. And don't forget herbs which can add interest and nutrients.