Applesauce, olive oil and canola oil can be used in place of vegetable oil depending on the cooking task. There are many of other substitutes for vegetable oil, such as bananas, butter and even yogurt.
Applesauce can be used in baked goods. Not only is it a healthier option than vegetable oil, it also replicates the moistness the oil provides. Olive oil can be used as a substitute in salad dressings. It's important to note that olive oil doesn't respond well to high levels of heat, so it isn't a good idea to use it in a stir-fry. Canola oil is a better option for fried foods.