Maybe 10 years ago, I could have called Nidoking my signature Pokemon.
Today, I like some variety in my teams. While my favorite Pokemon is clearly Magikarp, I still don't get one in every run. Because if you get the same Pokemon again each time, there's no point in starting a new game.
But, while I lack a signature Pokemon in that definition, I do have one in most runs, in this case the signature being the most reliable (and overused) teammember. Recent ones would be Poliwhirl or Fearow.