Typically, you fry eggs in canola or vegetable oil: fats with neutral flavor and a high smoke point, meaning you can cook the egg at medium-high heat and not worry about the oil smoking and giving the egg off flavors.
But you can easily add a little pizzazz to a simple fried egg by using flavored cooking oils. These oils have lower smoke points than canola, so you'll need to cook the egg over medium to medium-low heat. And because you're cooking with lower heat, make sure to use a nonstick pan to prevent sticking.
If you're a big fan of fried eggs with lacy brown, crispy edges, this method is not for you. But if you like your whites supple and tender, consider these alternative oils:
Sesame oil: Gives the egg a little Asian flair. Consider seasoning the cooked egg with a few drops of soy sauce and maybe a little sriracha, gochujang, or sambal oelek.
Avocado oil: Nutty, fruity flavor extracted from the exalted green fruit.
Walnut oil: Nutty (obvs). This is a good one for fried eggs that top green salads or asparagus.
Extra-virgin olive oil: Let's not forget this one, though choose wisely. Some EVOOs are very potently flavored and might overpower the egg. But those with subtle fruity or grassy notes might be just the thing.