I think any diet where the calories in are less than the calories out seem to work. However, I prefer the low-carb diet. If you keep your carbs low, then when you exercise you will be burning fat sooner. Even on a low carb diet, I still track my calories. I don't mind if a large percentage of my daily intake is from fat... as long as the total calories for the day are less than 2200. I try to keep carbs at less than 100 grams net (carbohydrates - fiber) per day. I think a person can lose weight by diet alone, however, exercise can really accelerate the process.
The one drawback of the low-carb diet is that in the beginning, for the first 2-4 weeks your energy levels seem to be lower. I believe it is your body adjusting to a new type of fuel... fat burning rather than carb burning. I've been at it for six weeks now and I'm seeing some really great results... I'm down 18 lbs. That's probably a little bit too fast of weight loss, but I think it will level off at 1.5 lbs - 2.5 lbs per week for the next 10-12 weeks.