I've heard that reusing cooking oil can be unhealthy. For example:
Never re-use cooking oil once it has been exposed to heat. It is a recipe for trans fats and cancer-causing carcinogens. -Source
Is this true?
Go Ask Alice, a Q&A site for health from Columbia University addressed this question:
Reusing cooking oil has been done for ages. There really isn't a problem, if done properly. The greatest hazard is allowing the fat to become rancid (spoiled) and deteriorated to the point it produces undesirable flavors and odors. Besides ruining what would have been a perfectly good meal, rancid oils also contain free radicals that are potentially carcinogenic.
However that entry is from 2002. Since then there have been studies that indicate the re-use of cooking oils can have detrimental effects on health:
Experts say that different types of cooking oils are better for you than others, and a new study suggests that the number of times you reuse cooking oils can also affect your health.
Spanish researchers found that people whose kitchens contained any type of oil that had been reused many times over were more likely to have high blood pressure than people whose cooking oils were changed more frequently.
A link to the study
A separate study in 2005 found that a toxin called 4-hydroxy-trans-2-nonenal (HNE) forms when cooking oils are reheated and has been associated with increased risks of stroke, Alzheimers, Huntingtons disease and other health problems.
Quoting from the study:
Previous investigations in this laboratory showed that HNE is formed in thermally oxidized soybean oil, which is high in linoleic acid. Continuous exposure of the oil to frying temperature (185°C) for up to 6 h graduallyincreased the formation of HNE and other polar lipophilic aldehydes. Additional investigations in this laboratory showed that HNE is absorbed into food fried in thermally oxidized oil in the same concentration as was found in the oil.
So, there is evidence that re-heating cooking oils can have a negative health impact. It is unclear to what extent the impact would be on humans at this stage. Given that the study experiments continuously heated the oil for an extended period, re-using cooking oil once or twice is probably OK.