Should King Ghidorah get his own movie?

Short answer: No

I think it would be cool.

Why not?!  I'd be down for some standalone kaiju films from Toho or perhaps Legendary, and King Ghidorah would be a great one to start with!  With all the serial "Cinematic Universe" series being made now, a series of Legendary-produced kaiju films that all tie back into the Godzilla series might be cool!  It'll most likely never happen, but in my book, more Kaiju films=better. ;)

YES!

Eh, I think King Ghidorah works best as a wild foil to another monster. Although, I'd love to see a movie where he exterminates worlds, particularly Venus from the Showa series. Won't happen, but it'd be one of the more interesting Godzilla spin-offs.

Should he? Probably, it would be really cool to give some insight into King Ghidorah's past and show how and why he exterminated so many worlds. Will it happen? Probably not. The only monster besides Godzilla with enough marquee value to get a spinoff is Mothra, and there alreasy was the Rebirth of Mothra trilogy.

It's kind of like giving the Joker or Lex Luther their own movies.

If done right, it can definitely work. There's enough of a backstory to work with (heck, with Ghidorah, we have 3 backstories) and the character is popular enough for the film to have a chance at making a good amount at the box office.

However, you also have that missing element: the relationship between the antagonist and the protagonist. Without Godzilla, Ghidorah is an adversary with no one to face. The gap would somehow need to be filled; whether it be with a human influence or another kaiju is debatable.

^I didn't think of that! :P

If there was a movie about him, than it would be very interisting.