Oregano is a staple in Greek cuisine, and if you cook a lot of food from that region, try your hand at growing Greek oregano, which has a stronger, more intense flavor than plants sold as Italian oregano (Origanum x majoricum, actually a cross between Greek Oregano and Marjoram).
My favorite dish to make with this variety of oregano is lemony Greek potatoes. You cut the potatoes the long way into thick wedges and toss them in olive oil. Spread the potatoes onto a baking sheet, top with snipped oregano leaves and squeeze on some lemon juice. Salt and pepper to taste, and bake at 450 degrees until the potatoes are cooked through.
Greek salad also highlights the flavor of oregano, which is a major flavor component in the dressing. Combine about a quarter cup of red wine vinegar with a tablespoon of Dijon mustard, and about a quarter cup of olive oil. Salt and pepper to taste, add a little garlic and at least a tablespoon of fresh oregano.
Oregano is also a main ingredient in Italian seasoning (hence the name Italian oregano), and you can sprinkle fresh oregano into most any Italian-style sauce.
Add extra oregano to your tomato sauce when you are making pizza (after all, oregano is sometimes referred to as the "pizza herb"). When your garden gives you an over-abundance of summer tomatoes, it is a good time to cook up a batch of pizza sauce and freeze it in one-cup portions to have on hand in the winter, when supermarket tomatoes are pink, at best. When I make pizza sauce, I like to get a huge pot bubbling, but you can sauce about three pizzas with the following: A small onion and four cloves of garlic sautéed until translucent. Add five or six cups of tomatoes, a little red wine, and a spoonful of sugar. Salt and pepper to taste, and add a teaspoon of oregano and a teaspoon of a mixture of rosemary, basil and parsley.
Oregano pairs well with a variety of cheeses, from provolone to feta and is especially tasty when the cheeses in question melt, allowing the herb's flavors to suffuse throughout the cheese. Try adding cheese and oregano to omelets, frittatas and other egg dishes.
Bean dishes also benefit from the addition of oregano. The herb is a "must" in traditional recipes for black bean soup, refried beans and charro beans. To make easy charro beans, soak a pound of pinto beans overnight, then toss in some onion tomato and garlic. Add some bacon or ham for flavor, some jalapenos for heat, and a goodly amount of oregano, and cook it down for a couple of hours.
Note: Oregano is used extensively in Mexican cooking. Mexican Oregano (Lippia graveolens) is a completely different plant with a surprisingly similar taste. You can sensibly substitute Greek or Italian Oregano in recipes that call for Mexican Oregano, even though they are not exactly the same. Mexican oregano tastes "earthier" than Italian or Greek Oregano. Mexican oregano is a key ingredient in chili powder.
Once you get a feel for the flavor Oregano adds to your food, you will start looking for other ways to use it. It is so common in in cuisines in widely-spread parts of the world precisely because it adds that "special something" to such a wide variety of ingredients.