Answer:
I'm not sure if you mean diet as in losing weight, or diet as in the type of food consumed. I'm going to go with the latter, for now.
Lacto-ovo Vegetarian
A lacto-ovo vegetarian is probably the vegetarian type you're most familiar with. This is someone who abstains from all meat products, but still eats products that animals produce - namely dairy (lacto) and eggs (ovo). I personally subscribe to this form of vegetarianism, as it fulfills my political and ethical reasons in becoming a vegetarian, but still allows me to get the nutrients I need effortlessly. And I love cheese.
Lacto Vegetarian
A lacto vegetarian is someone who abstains from all meat products - including eggs- but still consumes dairy.
Ovo Vegetarian
An ovo vegetarian is someone who abstains from all meat and dairy products, but still eats eggs.
Pescatarian
Pescatarians do not eat any meat products with the exception of fish, and still consume eggs and dairy. Many pescatarians I know do so because of the health benefits of fish - good, healthy fish is exceptionally good for you. Mercury build-up in fish fats though can have seriously detrimental effects on your nervous system, though, so consuming it on occasion is recommended.
Pollo-vegetarian
Pollo-vegetarians eat chicken products, but refrain from eating all other meats.
Vegan
Veganism is the practice of not consuming any product that comes from an animal, including meats, dairy, and eggs. Some vegans refrain from eating honey and refined sugar, but these are a point of debate and largely left to personal preference. Items of clothing - such as leather and fur - are also incorporated into some vegan "diets". There are a whole line of shops that advertise as being "vegan" that sell soy candles, vegan foods, and vegan clothing. So, if you choose this route, you're in good company!
Raw Foodist (aka Raw Veganism)
Raw foodists do not cook any of their food above 115 degrrees F, as they believe breaking this temperature loses nutritional value and can even become harmful to the body. The raw foodists diet is typically composed of legumes, vegetables, fruits, sprouts, nuts, and whole grains. Some even choose to consume meat, such as raw fish and other fermented meat products that purify naturally. This diet is recommended to only the most passionate folks, who are willing to watch their nutrient levels pretty carefully.
Macrobiotic
Those who choose to follow a macrobiotic diet eat mostly whole grains, vegetables, and legumes. They avoid highly processed foods as much as possible, eating foods that are large (macro) in life (biotic). This dietary regimen encompasses more than just food, and is more regarded as a lifestyle. It includes mental well-being and being acutely aware of the actual effects food have on your body and mind.