What is Fasting
Fasting is considered by some to be a type of diet, but it's more than that. Fasting is the process of eliminating food, drink or both for a period of time that is determined by the individual. This means complete abstinence from food and/or drinks other than water. This is why some consider fasting to be unhealthy. While it can be unhealthy if not approved and overlooked by a physician, it's normally, realtively safe for most people.
While intermittent fasting is a form of fasting over a set period of time (or window of time), fasting is more strict. Most people generally fast for 24-72 hours, although many prefer to go far longer than this. In fact, the longest fast in history was a 382 fast back in 1973. This is a bit complex, though, as this man had medical support during the entire fast, as well as the fact that he was extremely obese; so please do not think that this is normal in any way.
Fasting can definitely be longer than 24-72 hours though, and some people will actually fast several days a week, every week, for various reasons.
Medical Reasons for Fasting
Many people will fast due to medical reasons, such as pre-surgery that will require the use of anethesia, or testing for cholesterol or blood glucose levels.
Fasting prior to a surgery is necessary due to the risk of pulmonary aspiration of gastric contents after induction of anesthesia. 
Fasting: Beyond Health Reasons
There are many religions that have been fasting for centuries, with varying reasons for doing so. Religions that practice fasting include Roman Catholicism, Buddhism, Mormonism, Islam, Christianity, Judaism, Sikhism, Taoism and many more.
There are other reasons people fast, including during political statements. This is called a hunger strike and is used to cause guilt in most situations. This type of fasting has been used all over the world in some of the most well-documented historical events.
Some protestors include Cesar Chavez, Bobby Sands and, probably the most popular, Mohandas K. Gandhi.
Fasting can be a great way to lose a little extra fat. Your body will utilize fat cells for energy rather than relying on the food you eat. However, this should be taken with a grain of salt for many people as it really depends on your weight! Please consult with your physician before trying to fast.
If you have digestive issues you can also try fasting to give your digestive system a break every once in a while. It has worked wonders for myself.
Fasting can also be used to break bad habits, such as food, drinking, smoking, drugs and more.
Should You Fast
Without medical guidance, I would suggest that you do not fast for more than a day or two. You would probably be okay for a little more time than that, but without knowing your medical conditions I would not suggest anymore than 24-48 hours.
Fasting can be used to not just help you lose weight, but it can also be a great way to give your system a temporary break from digesting food, which makes it more important to try small fasts, especially if you suffer from issues with indigestion.
Again, please consult with your physician before trying to fast.