I think it kinda depends on the movies in question and how old your kids are. I started watching horror movies very young – aged 4 or 5 when I saw the first horror flicks that I vividly remember. My parents watched any good rated English language films back in the day because we had very little choice back then, depending on a video lending library to get us some movies to watch and the odd Sunday night movie that we got on tv (no cable) back in the early 80s.
So yeah I did watch them, hiding partially behind the sofa though. Before I turned 10 I remember that I had watched a few more horror classics that I absolutely love now. But each time I had an adult with me, either my parents or some uncles/aunts along with my cousins in India. In the case of my cousins and I, we got scared together. There’s some comfort in that shared fear. But those are the movies that I hold near & dear to my heart because, while they are awesome movies, it also reminds me of great times with my extended family.
I wouldn’t advise bloody & gory stuff or body horror/slasher porn films to be shown to kids under the age of 16. You could screw up some of their poor brains at an early age. I would advise parental guidance in terms of being there and offering some support if they get too scared. Ghosts, goblins, werewolves, zombies and the boogeyman are ok – but some movies might be too much for the young. Choose wisely.