It depends on the temperature. Olive oil should be fine if it's not smoking or close to smoking (same rule for all oils).
Personally, I don't cook with olive oil, just use gallons of the stuff on salads and in shot glasses. Most of my cooking is with grassfed butter, and with pork fat or beef tallow when I can. For high heat cooking clarified butter is top notch. Coconut oil can be good for stir-fry mixups, but I get tired of the coconuty taste if it doesn't blend under the flavor of the dish/spices. Red palm oil (not palm kernel) is another wonderful oil for more exotic cooking or eating with a spoon. Along with avocado and coconut milk, I rotate through those fats on a random basis to keep happiness a'flowin.
Specifically for a frying pan, I'd use the more saturated animal fats or clarified butter, as they're stable at much higher heats than the mainly monounsaturated oils like olive oil. Coconut and red palm are saturated and stable at high heat too, but their flavors keep them from normal frying duty in my kitchen.
Last edited by Tyler Micheli; 07-14-2010 at 08:08 PM.