This summer, I lost 11 pounds on the South Beach diet--in 5 days. Unfortunately, after the third day, I barely had the energy to get up off the couch (I'd been trying to implement an exercise program, too, but every time I stood up, I got dizzy and saw bright spots before me). On the fifth day, I passed out on my way to the bathroom. After I got up, I went to the kitchen, made myself a peanut butter and jelly sandwich (on wheat bread), and felt stronger within an hour.
I had my suspicions about what was going on, so I did some research and discovered that I was right. I am hypoglycemic, which I thought was odd, considering I am a bit overweight. Nevertheless, severely restricting carbs from my diet, even for only 5 days, made my blood sugar absolutely bottom out to the point of causing me to become unconscious for a few seconds. Not good at all. I don't recommend the Atkins or South Beach diet to anyone who is hypoglycemic. My advice to anyone is that if they do become weak to stop the diet, or at least back off of it a little bit. The weakened state of your body makes it impossible to exercise, which is a key factor in weight loss. (Also, like any diet, much of the initial weight loss is due to water loss.)
As a side note, weight loss/gain is due to the ratio of calorie intake and calorie expenditure. The Atkins and South Beach diets, especially in the first phases, severely restrict carbohydrates, which have 4 calories per gram, and encourage the intake of eggs, meat, etc., which contain a good deal of fat, which has 9 calories per gram. So according to the calories in/calories out "model," a person can eat more than twice the amount of carbohydrates as fats with the exact same calorie intake. Just something to think about.
That said, I know there are people who can stick to the Atkins or South Beach diet, and none of them have experienced the "side effects" that I did. If either of these diets work for you, I congratulate you on having more willpower than I did!

And as someone else said before, "Find what works for you and stick with it!"
Edited because I'm a perfectionist! LOL