What oil or fat to use for different purposes?

"Commonly used" depends mostly on the culture, I'd assume. There's a lot of different oils, so I've organized by use rather than try for a complete list.

Some of the ones that you might find in a "typical American" foodie's kitchen include:

For frying: something with a high smoke point : peanut, sunflower, soy, extra light olive oil

For baking (muffins & cakes): something with a mild flavor : corn, canola, "vegetable", soy

For baking (biscuits & pastry, or greasing a pan) something solid at room temp : butter, shortening, lard

For general pan cooking: olive oil (any kind), butter, anything from the "baking (muffins)" list. update: this assumes sautéing heat or lower; see 'frying' for higher heat applications.

For salad dressing: any nut oil, mild oil, or virgin / extra virgin olive oil

For sauces: Butter.

For finishing: something flavorful to drizzle over at the last second... odds are, it's extra virgin olive oil, but possibly sesame or a nut oil.

Now, there's regional differences -- in the south, it's pretty common to save your bacon grease for cooking and to use shortening for frying. Lard's still popular in hispanic (and likely other) cuisine, schmaltz (rendered poultry fat) is used in both Jewish and French cooking. Ghee (similar to clarified butter), is used Indian cuisine ... and the list goes on.

If you're looking for a 'must keep on hand' list -- a mild oil, extra virgin olive oil and butter will get you through most anything. Add shortening if you like baking, and sesame oil if you like to cook asian food, and you'll be prepared for most anything.

There are a great many oils and fats on the market, which you choose to use will largely depend on several factors:

• Type of cuisine being prepared
• Health considerations
• Flavour profile required

The most common oils are probably

• Olive oil - This is a great oil for preparing a whole variety of foods, it's also great in salads. It typically comes in four varieties:

• Extra Virgin

• Virgin

• Refined

• Extra Light

Olive oil has numerous health benefits and is great for the heart. Olive oil has a smoke point range between 208c for Extra virgin and 243c for Extra Light.

Sunflower oil - A good all purpose oil, useful for cooking and salads. Sunflower oil has a smoke point of 226c

Corn oil - Not a great deal of taste but is great for frying. it's also not terribly healthy. Corn oil has a smoke point of 233c

Peanut oil - My favourite when cooking Asian food. Peanut oil has a smoke point of 225c.

Butter is also commonly used in cooking either alone or with oil. Butter brings a richness to sauces, it's also great for adding at the end of the cooking process to add a little sweetness and shine to the food. Butter has a smoke point of 150c.

Another form of butter, referred to as clarified butter or ghee is used in the preparation of Indian food. it has a slightly nutty flavour and a high smoke point. I nearly always make my own but you can buy it. Ghee has a smoke point range between 190c and 250c.

It addition to the aforementioned oils, there are a number of 'specialist' oils that are fantastic in salads:

• Walnut oil
• Hazelnut oil
• Sesame oil

All of these have a very distinctive flavour and should be used in moderation. sesame oil is really great in Asian food. Add a little sesame oil with the peanut oil for cooking or add a little towards the end.

Edit: I forgot to mention lard. Lard is used in a variety of cooking processes, including baking and frying. It has a relatively high smoke pint, which makes it ideal for deep frying. It's also used in a process called larding, where small amounts of lard or lardons from bacon fat are injected into lean meat by means of a larding needle.

• Peanut or sunflower oil: high smoking point, good for frying
• Clarified butter: similar to above but more flavor
• Olive oil: a lot of taste, extra-virgin oil burns quickly
• Butter: low smoking point, I usually use it for sauteing at low heat, e.g. garlic

here on the wiki you can find table of cooking oils and their usage purposes: