Dieting has so many fads: weight watchers, no carbs, etc. What is actually working or the healthiest? And do european body wraps actually work?

Calorie is a calorie. Helpful weight loss diets include natural foods that take time to chew but contain few calories. Examples include carrots, celery, and iceberg lettuce (without salad dressing). If fad diet foods fall into this category, and a person eats fewer calories than he uses each day, he will lose weight. A calorie is a calorie, regardless of where it comes from. Wraps do not decrease one's calorie intake.
See below. While calories in calories out is part of the story it is not the whole story. Eating a diet high in refined simple sugars and foods with a high glycemic index cause our Insulin levels to remain elevated. High levels of Insulin prevent us from utilizing fat for energy. This is why most diabetics get fatter when they start on insulin. Reducing the amount of simple sugars that we eat is important.