Considering the smoking point of the oil you're using is probably the most important thing when choosing an oil. The smoke point is generally regarded as the 'maximum usable temperature' for a given oil. Oils begin to break down when they get hot enough to 'smoke' and the nutritional benefits are diminished significantly (or they can become toxic). When I'm spending the money to use an alternative, healthy oil, I want to be sure that the health benefit isn't lost by by the time my food gets to the table. If I'm going cheap and using a processed, mainstream oil, I also want to consider the smoke point because I am wary about what it will turn into once it starts breaking down.
Understanding the fat profile of your oil choice is also important. Most people understand that trans fats are bad for you. Natural saturated fats like those found in butter or coconut oil are the subject of much debate. After reading Nourishing Traditions, I feel very comfortable using a lot of these in our diet. Unsaturated fats - the omega 3, 6, and 9s - can also be great oil choices but sorting thru the choices in this category can be confusing. Omega simply refers to the end of the carbon chain (as in, alpha and omega). The corresponding number refers to where the first double bond occurs on the chain when counting from the 'omega' side. So on an omega 3 fatty acid, there is a double bond on the 3rd carbon when you count from the end. Phew, aren't you glad to have that straight?
Omega 3s are AWESOME. Eat more of them. Fish oil and flaxseed oil are packed with omega 3s. These oils have very low smoke points (235' and 225' respectively) and should not be used to cook with. Corn, soybean, olive, canola, macadamia nut and walnut all have small amounts of omega 3s and have higher smoke points. Be sure to research the processing methods of these oils because if they use high temperatures, the Omega 3s will go rancid and no longer be of benefit to you (or even become toxic).
Omega 6s are poly-unsaturated fats. They are good for you but only when they're balanced with enough Omega 3s. Ideally, you want as low of a ratio as possible. 1:1 is ideal but anything under 1:12 is still considered good. The problem is, we tend to eat a ton of the omega 6s without balancing them out with the omega 3s so our ratio tends to be closer to 1:20 - if we're lucky. Choosing an oil that's low in Omega 6s is going to do the least amount of damage to your omega 3:6 ratio. Oils high in Omega 6 also go rancid easily so be wary of the temperatures used in processing.
Omega 9s are mono-unsaturated fats. The American Heart association recommends that 80% of your fat come from omega-9 fatty acids (if you're not following the Nourishing Traditions ideal). Oleic acid is a type of mono-unsaturated fat and is very healthy for you. Supposedly, your body also produces these omega-9s on it's own but I haven't really looked into that.
To sum up, choose an oil that has a high enough smoke point for what you're trying to cook. Try to use natural fats like butter or coconut oil or choose an oil that has a good omega 3:6 ratio. If you're cooking at a higher temperature and can't choose an oil with any omega 3s, choose one that's high in omega 9s or use butter.
Olive oil seems to be everyone's favorite choice. It is a very healthy oil with a decent omega 3:6 ratio (1:12) and high omega-9s (72%). It's also readily available at the store - this is a big plus. But supposedly the labeling of olive oils isn't well regulated. Apparently some manufacturers mix refined and virgin oils together to lower the acidity and qualify for an extra-virgin rating. Others supposedly ship their product to Italy to get labeled as an Italian product. So don't be automatically go for the cheap evoo unless you know where it's coming from. With this product, you probably need to pay the price to get the real deal. Another problem is that its smoking point is 300'F, so I can't use it reliably for anything cooked at a higher temperature than that, or anything sauted on high. Olive oil is best used cold or with low to medium-low temperature cooking.
Oils with higher smoke points don't tend to have any omega 3s but there are still some good choices. Avocado oil and Hazelnut oil both have high smoke points (520' and 425' respectively) and low omega 6s. Grapeseed oil is another good choice because of its high smoke point (400') but it is high in omega 6s and therefor low in omega 9s - and it tastes really 'clean'.
I know you're all waiting for me to mention canola oil. I suppose I do need to tackle it for a sense of completeness. The smoke point on canola oil is 350'F. It has a 1:2.4 ratio of omega 3:6s and only 12% saturated fat. But it's very processed. The rapeseeds are exposed to high temperatures and chemicals during the processes of refining, bleaching, de-gumming, and finally deodorization (to remove the awful smell that happens when omega-3s go rancid under high temperatures). Also, the trans fat content is listed at 0.2 on the label but research at the U of Florida at Gainesville showed levels up to 4.6 in commercial liquid canola oil. So, personally, I am very leery of this oil. The fact that more than 80% of the plants used are GMOs doesn't help my opinion of it either.
Macadamia Nut oil is supposedly the best thing out there. Its smoke point is 410'F. It has super high omega 9s (84)% and an unheard of 1:1 ratio on the omega 3:6s. It's also crazy expensive and hard to find. I did finally find it at a health food store here in LA and it's been fun to use. It adds a nice nutty flavor to simple dishes.
My cupboard has extra virgin olive oil, macadamia nut, and coconut oil in it. I have also started using a lot more butter (read Nourishing Traditions to find out why). I have used and enjoyed grapeseed oil. It's cheaper than many other non-standard oils so that was a starting point for me. Coconut oil has a smoke point of 450'F and has medium chain, not long chain fatty acids. And truth be told, I still have a gallon of vegetable oil in the way back on the bottom - but it's just there for food storage in case of an emergency, until I can ramp up my supply of the others. I don't actually use the stuff.
I have made some efforts to reduce our oil consumption so I can afford the nicer oils. I mostly use it in my bread, salad dressings, and for sauteing. Other recipes that call for a noticeable amount of oil, I just don't make that often. Other good strategies are replacing half the fat with applesauce or replacing it entirely with white bean mush. Brownies are surprisingly good with blended up black beans. Or just use butter :)
Note: Updated 5/3/10 after reading Nourishing Traditions by Sally Fallon and Mary Enig