What vegetables oils are safe to use at high temperatures (350, maybe 400 F) , say, stir fry or pan-frying chicken/fish?
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:


Peanut - 450 F / 232 C
Grapeseed - 420 F / 216 C
Avocado - 375 F / 190 C


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:


Cooking Fats 101: What Makes Fats and Oils Essential to Cooking
Cooking Fats 101: What's a Smoke Point and Why Does it Matter?