Electrical Safety

TVs and computer or video monitors are among the more dangerous of consumer electronic equipment when it comes to servicing. There are two areas which have particularly nasty electrical dangers: the non-isolated line power supply and the CRT high voltage.
Major parts of nearly all modern TVs and many computer monitors are directly connected to the AC line - there is no power transformer to provide the essential barrier for safety and to minimize the risk of equipment damage. In the majority of designs, the live parts of the TV or monitor are limited to the AC input and line filter, degauss circuit, bridge rectifier and main filter capacitors, low voltage regulator, horizontal output transistor and primary side of the flyback transformer, and parts of the startup circuit and standby power supply. The flyback generates most of the other voltages used in the unit and provides an isolation barrier so that the signal circuits are not line connected and safer.
Since a bridge rectifier is generally used in the power supply, both directions of the polarized plug result in dangerous conditions and an isolation transformer really should be used - to protect you, your test equipment, and the TV, from serious damage. Some TVs do not have any isolation barrier whatsoever - the entire chassis is live. These are particularly nasty.
The high voltage to the CRT, while 200 times greater than the line input, is not nearly as dangerous for several reasons. First, it is present in a very limited area of the TV or monitor - from the output of the flyback to the CRT anode via the fat red wire and suction cup connector. If you don't need to remove the mainboard or replace the flyback or CRT, then leave it alone and it should not bite. Furthermore, while the shock from the HV can be quite painful due to the capacitance of the CRT envelope, it is not nearly as likely to be lethal since the current available from the line connected power supply is much greater.