Oils and fats are basic nutrients, and not simply sources of calories. Although all fats and oils have the same number of calories (9 kilo-calories per gram), there are substantial differences in the three types of fats: saturated, monounsaturated and polyunsaturated.

Saturated fats (SAFAs) come mostly from animal sources. They have normally high melting points and are usually solid at room temperatures. They are also storage fats, designed for hunters' days of want, not the affluence of modern consumers. Eat with forethought and deliberate prudence. Especially, if you had a fat or chubby childhood.
Monounsaturated fats (MUFAs) are olive oil, canola oil, and some difficult to find and expensive oils like almond, hazel nut, etc. They are usually liquid at room temperature. MUFAs can reduce total blood cholesterol without affecting good HDL cholesterol. They are fine antioxidants that help prevent and treat many food related degenerative diseases.
Polyunsaturated fats (PUFAs) are most seed oils, like corn, safflower, sesame, soybean, and sunflower oils. PUFAs like MUFAs are also liquid at room temperature. PUFAs belong to the omega-6 series of fatty acids, a certain amount of which is essential, but an excess of which is decidedly unhealthy. Here balance is of the essence (see below).
Superunsaturated fats (SUFAs) are also PUFAs but with a greater potential for health. They are mostly fish oils, like eicosapentanoic acid (EPA) and docosahexanoic acid (DHA). It is because of fish oils in their diets, that Eskimos were nearly free of heart disease, despite their high fat diets. SUFAs help reduce the storage fats in our blood known as triglycerides, prevent arteriosclerosis, arthritis, heart disease, high blood pressure, some forms of cancer, inflammatory and autoimmune diseases, etc.

Cold pressed olive oil or canola oil for their MUFAs, a seed oil for PUFAs, and fresh flax oil for its omega-3 SUFAs. If you cannot get flax oil, eat fat fish twice a week if that is at all possible. Try to get all these oils, as all are needed for sound health, but try to balance PUFAs to SUFAs in a 3:1 ratio or so. Give always preference to oil stored in opaque containers, as light can denature oil molecules a thousand times faster than darkness. And remember oils and fats have more calories than other foods, so use some discretion.

Saturated fats like butter; refined and processed oils; hydrogenated margarines; other hardened oils; shortenings, etc.