It’s not something you think about, but your television is always running “hot,” so that the picture will come on the instant you press the power button. To do that, the TV has power stored in capacitors at all times (even when it’s “off”). As you say, only by unplugging it, or turning off the surge protector, can you be assured the television is not consuming electricity.

A surge protector is a very good idea, but remember that you need to run your cable or satellite signal line through it as well to be fully protected. Lightning is much more likely to come in through your cable or phone line than the power line.