I've read in a number books that at high temperatures vegetable oils oxidize.
Also, some vegetable oils (I have heard) are processed at high temperatures so they may already be in the same state as the above.
What vegetable oils are suitable for high temperature cooking?
Actual oxidation of the oils is a major contributor to rancidity, which would render the oil extremely unpalatable and therefore unsuitable for cooking.
The efficacy of oil at higher temperatures is related to its smoke point, which Wikipedia defines as:
the temperature at which, under defined conditions, enough volatile compounds emerge from the oil that a bluish smoke becomes clearly visible
In general you want to use oils below their smoke point, or just barely at it.
The smoke point for different culinary fats depends on their composition, and the amount of refining and removing of impurities within.
Some oils which offer superior performance at high smoke points include:
You also generally want to choose a refined, neutrally flavored oil for most such applications.
For more data, please see the linked Wikipedia article, or the compilation at the Good Eats fan pages.
Update: for a good treatise on cooking with fat or oil, see the series in progress at Serious Eats:
Rapeseed oil (Canola in the States) has a smoke point of 240 deg C, beaten only by Sunflower Oil at 246 deg.C. Rapeseed oil is processed with heat unless it is sold as cold pressed, premium, virgin or extra virgin. Unfortunately, if you're in the States, the product sold as 'Canola' will contain partially hydrogenated fats, and will most likely be from GM crops. In the UK, rapeseed oil contains no hydrogenated fats, nor is it currently genetically modified, though this may be of no importance to you either way.
Seems like safflower oil or light olive oil are best. Beyond that, "refined" is better than "unrefined" as far as smoke point.
I looked at a few sites:
http://en.wikipedia.org/wiki/Smoke_point
http://healthyeating.sfgate.com/good-bad-cooking-oils-9051.html
http://www.cookingforengineers.com/article/50/Smoke-Points-of-Various-Fats
