Basically, NONE.

A 2002 report of the Institute of Medicine (part of the National Academy of Sciences) concluded that trans fats "are not essential and provide no known benefit to human health." In addition, the report emphasized that "there is a positive linear trend between trans fatty acid intake and LDL cholesterol concentration, and therefore increased risk of CHD [coronary heart disease]." This means that the more trans fat you eat, the more you increase your risk of heart disease, even at very small levels of consumption.

The report did not establish a recommended daily allowance of trans fats "because any incremental increase in trans fatty acid intake increases CHD risk." The report instead recommended that "trans fatty acid consumption be as low as possible while consuming a nutritionally adequate diet."

You can view the full report at Institute of Medicine (part of the National Academy of Sciences.