Medical emergency

A medical emergency is an injury or illness that poses an immediate threat to a person's long-term health or life. It needs to be treated immediately. Doctors that are trained in emergency medicine are taught how to react to medical emergencies, and how to resuscitate patients.
Response
When there is a medical emergency, emergency medical services should be notified as soon as possible by calling for help using a local emergency telephone number, such as 911 in the United States or Canada, 112 in most of continental Europe and on GSM cell phones, 999 in the UK and most of its former colonies (112 works as well), 15 in France, 118 in Italy, 119 in South Korea and Japan, 000 in Australia, 101 in Israel and 111 in New Zealand. Calls to emergency services are usually free of charge; they can be made from any phone; in the case of a prepaid phone no credit is required.
The people that answer emergency calls, emergency medical dispatchers, will ask questions about the person who needs immediate treatment; some of the questions are whether the person is conscious, how badly injured they are, their name if it is known, and if they have any other illnesses. They will also ask some basic information about the called, such as the name of the person calling.
Many countries have laws that require anyone to help those in immediate danger. Help can mean as little as alerting emergency services, or telling other people that the person is having a problem. People that know first aid are expected to help as much as they can. Moving the victim to a safe place can sometimes do more harm than good, and should be left to people that know how to properly move injured people unless there is no alternative (for example, in wilderness first aid). Many states have laws that protect those helping.
If the victim is not breathing, or if a heartbeat cannot be felt, artificial respiration and cardiopulmonary resuscitation (CPR) could be needed to keep a person's blood circulating long enough for medics to attempt revival. Emergency medical technicians, Outdoor Emergency Care technicians or paramedics can use airway management techniques to help a person who is not breathing.
Clinical response
While in a hospital environment, staff members that are on duty are trained to deal with emergency situations. Emergency medical physicians are trained to deal with many medical emergencies, and have up-to-date cardiopulmonary resuscitation and advanced cardiac life support certificates. In major incidents, most hospitals have protocols to have staff that are not at work at the hospital to go on duty as fast as they can.
Emergency departments follow basic advanced cardiac life support protocols, which include keeping a patient's blood pressure and blood saturation at acceptable levels. Possible exceptions include the clamping of arteries in severe haemorrhage.
Statistics
Most emergencies are quite unspectacular. They will happen close to home.
53% happen at home (or when doing a hobby)
15% happen at school
6% are traffic accidents
Of all emergencies:
49% are illnesses (like a stroke, cardiac arrest or other problems with the heart)
10% are intoxications (like alcohol or other drugs)
12% are accidents (traffic accidents, accidents in the house)
17% are other things (for example, delivering a baby)
15% are false alarms (it looked like an emergency, but it really wasn't).