A ketogenic diet is not necessarily a zero carb diet. On a ketogenic diet, you can eat enough green vegetables and even a few berries and stay in a range of 20-50 carbs per day.
Eating a zero carb plan basically means you eat nothing but meat and fat and nothing else. No egg yolks, no dairy, no vegetables or fruit can be included as they contain carbohydrates. And actually, even meat has some carb because of the stored glycogen in the muscle.
It's a strange way to eat, but there are some people who swear by a zero carb diet and feel it is the healthiest way to eat. For instance, a man name Lex Rooker has been eating a zero carb regimen for several years now, and writes about it here. He insists he has experienced excellent health benefits from eating this way, but be aware he eats nothing but raw meat. He does not cook the meat he eats, as cooking changes the nutritional value of the food.
And this blog is all about eating zero carb by a woman named Kelly who feels it has been very beneficial for her. She started out her journey by eating low carb, and lost 130 pounds. Over time, she has found that zero carb works best for her.
In addition, the Inuit tribes of Alaska eat a zero carb diet for much of the year, and they have excellent health as well. The difference though, is that the meat they eat is clean. It comes from wild animals which have been fed on natural diets. They also eat the whole animal, and they eat a lot of it in the raw state (meat, organs, the fat, and stomach contents included) not just the muscle meat.
In America, unless you want to spend a small fortune on grass fed meat and chicken, and learn to like all parts of the animals you eat, it may not be the healthiest to go zero carb. Cooking meat destroys much of the vitamin content, so eating meat raw or almost raw is the most likely way you'll get enough vitamin C and other vitamins.
Jan Kwasniewski, a Polish physician who has designed a low carb diet which he calls Optimal Nutrition, has written that one should eat enough carbohydrate to avoid heavy ketosis. This post at Hyperlipid discusses Kwasniewski and ketosis.
There is some evidence that zero carb has the unintended effect of causing thyroid issues in converting T4 hormone to T3 hormone. Dr. Ron Rosedale thinks this is a normal response and writes that this slowing of the metabolism is a good thing for slowing aging.
Mark Sisson over at the Daily Apple writes about zero carb here.
In my personal experience, I feel best when my carb intake is between 10-40 carbs. For me, focusing on keeping my insulin low is what works, and when my carb intake is too low, I find my blood sugar starts to creep up via gluconeogenesis and a phenomenon called physiological insulin resistance.
However, some people do well on zero carb, and I think it's an individual call. You have to determine what your body response is to long term total carb restriction.