Answering this because neither of the other answers address a couple points regarding when High Jump Kick is used on a Ghost-type.
The High Jump Kick user taking damage when using it on a Ghost-type is dependent on the generation (and a couple other factors)
In Generations 1 through 3, High Jump Kick will not make the user take crash damage when used on a Ghost-type. In Generations 4 onward, High Jump Kick will make the user take damage when used on a Ghost-type.
Source
I'd also like to mention that there are other things that can contribute to High Jump Kick not being able to make the user take crash damage when used on a Ghost-type. High Jump Kick will not make the user take crash damage on a Ghost-type if the Ghost-type was hit by Foresight or Odor Sleuth, or the Ghost-type is holding Ring Target. A Pokemon with Scrappy that has High Jump Kick (Mega Lopunny moment) will not take crash damage when using it on a Ghost-type.