Cooking oil

Olive oil

Of all the different types of oils, olive oil is the healthiest one you can choose. It's highest in monounsaturated fat, which raises your HDL (healthy high density cholesterol), improves your arteries, and lowers your LDL (lousy low density cholesterol). Olive oil is rich in polyphenols and antioxidants, which will protect your cells against damage that can lead to cancer and heart disease. It also contains the anti-inflammatory compound oleocanthal. Extra virgin olive oil is the good stuff, it contains a high proportion of the plant extracts making it healthier, tastier, and more expensive than other olive oils. Cooking reduces the flavor and health benefits, so save the extra virgin for salad dressings, bread, and pasta. When sauteing or grilling go for the refined version, virgin olive oil, it'll be more cost effective.

Other oils

If you want a more neutral flavor, canola oil is a healthy (mostly monounsaturated fat) alternative to olive oil.

Nut and seed oils are good for the occasional seasoning of dishes. However, it's good to know the smoke point of oils so you don't degrade the oil, creating free radicals and other harmful chemicals. Also, oils that are high in polyunsaturated fat (soy, corn, vegetable, sunflower) form the compound HNE when they're heated. HNE gets into food that's cooked in the oil, then is processed in our bodies. In high concentrations, this compound messes with the activation of caspase enzymes or "executioner proteins" (plays a role in programmed cell death), the laddering of DNA, and releases cytochrome c from mitochondria (too complicated to explain but it's very important in making ATP, our fuel). It's being considered as a causal agent for numerous diseases. And if your fried chicken was in the 150th batch fried in reused oil you'll be consuming way more HNE than the guy who got the 1st.