The United States Food and Drug Administration (FDA) requires trans-fats to be listed on Nutrition Facts labels of packaged foods, but only when there is more than 0.5 grams trans-fat per serving. The "per serving" is the key to the problem. If a food product has less than 0.5 grams trans-fat per serving, the label will show zero grams trans-fats even if partially hydrogenated oil is one of the ingredients.
Partially hydrogenated oils are liquid polyunsaturated fat that have been treated with hydrogen molecules to create a semi-solid texture (like some types of stick margarine) and to improve storage time. The process changes the chemical shape of some of the fatty acids into trans-fats, which resemble saturated fat, except they're even worse for your health. Because of potential health issues, the amount of trans-fats must be listed on the Nutrition Facts labels, but as I stated, that can be a little deceiving.
If the labels says the food is trans-fat free, but the ingredients list includes partially hydrogenated oils, then you might have a problem. If you're going to eat a whole bag of chips fried in partially-hydrogenated oil, then you're going to get some trans-fats. It's difficult, then, to know exactly how much trans-fat you're consuming, so it's best to choose products that don't have any partially hydrogenated oils listed on the package.
United States Food and Drug Administration. "Trans-fat Now Listed with Saturated Fat and Cholesterol on the Nutrition Facts Label." Accessed February 12, 2008. http://www.fda.gov/Food/LabelingNutrition/ConsumerInformation/ucm109832.htm.