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Most current researchers agree that it's not fat that makes us fat. Moreover, it is the fat content of a meal that gives a sustained feeling of being satisfied. There's pretty much universal agreement that trans-fats (hydrogenated fats) are to be avoided. Beyond that, there are differences in low carb programs. 

For instance, both the Atkins Nutritional Approach and the Dr. Bernstein Diabetes Solution, are fairly liberal about fat intake. While mono-saturated and omega fats are encouraged, the Atkins plan encourages moderate use of full fat cheeses. The South Beach diet, by contrast, seeks to limit saturated fat, calling for "low fat" cheeses, etc. On a daily basis, most low carb plans do result in fat being the largest proportion of macro-nutrients ingested, followed by protein, with carbohydrates - high fiber ones - bringing up the rear.