Dirt, dust and grime build-up can be expensive, especially in your kitchen. Your refrigerator is a prime example. When the condenser coils behind or under your refrigerator get dirty, the compressor runs longer and hotter. This can have some surprising repercussions. It's easy to see that you'll use more energy when your refrigerator is cycling on more often, but it'll also be making your kitchen hotter. If it's summer, that means your air conditioner will need to run longer to process all that hot air. It's a double whammy. Oh, and because your fridge is working inefficiently, the compressor may burn out faster, too.
The refrigerator door gasket is another place where cleanliness matters. When the gasket is clean, it makes a good seal between the door and the cold box. When the gasket is dirty, it allows a little warm air to leak in, forcing the refrigerator to work harder to maintain its interior temperature. This uses energy and puts your food (especially items stored on the door) at risk. It also shortens the life of what's probably the most expensive appliance in your home.
Let's move to the stove. If you have stovetop reflectors under your electric burners, they're there for more than decoration. They actually help to reflect the heat from the element back up to your pot or pan. When they're dirty, they don't do the job as well, so it takes additional energy (and time) to cook food on your stovetop. There's more. Your oven is a marvel of design; it isn't just a big box that warms up when you turn a nob. The interior sides and bottom are actually designed to reflect heat onto your food. When your oven is covered in baked on gunk, it uses more energy and cooks food less evenly. In essence, you'll be paying more to prepare a roast that's overcooked -- but only on one side.