Tesla coils and their support equipment are extremely dangerous!
There are many known and unknown dangers associated with this type of equipment. "Some" of the known dangers are as follows:
High Voltages and Currents: Tesla coils use and produce extraordinarily high voltages and currents. Output voltages for small coils are typically in the range of 500,000 to 1,000,000 volts. Currents of 1000 to 5000 amperes may be present in the input circuits. Under no circumstances should one come into contact with these voltages and currents. In all cases the voltages and currents used in Tesla coils are considered far beyond lethal levels. Please see special note.
Burns: Due to the high frequencies involved, Tesla coils can cause severe burns without the sensation of pain. These burns are typically very deep and need long term medical attention.
Long Distance Arcing: Tesla coils, by their nature, produce electrical arcing which can travel unpredictably in any direction and can strike at considerable distances. These arcs can be very dangerous.
Electromagnetic Fields: Tesla coil type equipment produced extreme magnetic, electrostatic, and radio frequency fields. These may interfere with pacemakers and any other critical electronic devices in the area. These effects are unpredictable.
Ozone: Tesla coil equipment produces large quantities of ozone, which is poisonous. Adequate ventilation must always be maintained.
Ultraviolet Light: Spark gaps used in Tesla equipment produce intense ultraviolet light. This light can burn the retina of the eye with ease. Always cover any exposed arcs.
Fire: Tesla coils can and have started a number of fires. They can arc to flammable objects with ease. Any fire extinguishing equipment must be rated for electrical fires but still must only be used when the power is removed from this type of extremely high voltage equipment.
PCB Oil: Although rarely used now, high voltage devices such as transformers and capacitors may use oils containing PCBs. These substances can cause very serious and long-term heath problems and fatal cancers.
Explosions: Components used in Tesla coils can explode with great violence. High voltage capacitors especially can store a tremendous amount of energy and can fail catastrophically. Always wear eye protection and physically shield energy storage components.
Energy Storage: Tesla coil circuits can store lethal voltages long after external power sources are removed. Circuits can spontaneously become energized without warning. Power supplies and especially high voltage capacitors must be discharged before approaching this type of equipment.
X-rays: Vacuum tubes, light bulbs, and other evacuated spaces will produce X-rays when exposed to high voltages.
Radio Frequency Interference: Tesla coils always produce intense radio frequency interference.
Electronic Equipment Damage: Tesla coils can easily destroy any type of electronic equipment in the area or connected through the common AC wiring. This includes Computers, Televisions, etc.
There are a number of photographs both historical and modern that show people in close proximity to Tesla coils while they are in operation. In all cases these are either faked or done under very special circumstances. The most famous and unfortunate of these is shown here:
This and similar pictures give the impression that Tesla coils are safe. This picture is a double exposure. The following is an excerpt from Teslas notes "To give an idea of the magnitude of the discharge the experimenter is sitting slightly behind the "extra coil". I did not like this idea but some people find such photographs interesting. Of course, the discharge was not playing when the experimenter was photographed, as might be imagined!" Tesla and the photographer went to great lengths planning how they would produce these pictures using camera tricks. Other photographs show people with streamers flying out of their heads and such. This is extraordinarily risky. It should also be pointed out that modern designs are capable of producing and maintaining vastly higher power levels than some historic machines (not Teslas!).
Some explanation is in order.
We now know that the "skin effect" DOES NOT apply to people. RF currents travel easily within the body favoring nerves and blood vessels as current conductors!!! The effects of high energy pulsed RF inside the body is unknown... RF currents do not stimulate nerves. Therefore, one can have high frequency electric currents flowing through the body without feeling anything. Numerous accounts of people being burned by high frequency currents state that they first "smelled something burning!".
RF (Radio Frequency) burns are nasty! As the skin carbonizes the current burns into the body without any sensation. By the time you find out where all the smoke is coming from you have a hole burned in you. Typically this will require skin surgery to remove the destroyed flesh and close the wound.
To make a long story short. Stay far away from these devices when they are operating!