Let me begin this post by stating - "We horror fans are NOT a monolith."
Horror is more nuanced than the general public perceives. A wee babe in the horror community, I often find myself discussing films with friends and coworkers who dismiss the mention of the genre with a shake of the head and a simple, "I don't DO horror". What they really mean to say is "I don't enjoy gore and/or torture porn". Neither do I - but that doesn't really represent the best that horror has to offer.
Horror is simply defined as a "very strong feeling of fear, dread, and shock"
While gore can get the job done, it isn't the only thing that can inspire such reactions - not by a long shot! Some of the best horror films, be they classics or new releases, feature hardly any blood, focusing on giving you the psychological heebie jeebies rather than a stomach churning gross out session.
My favorite horror films deal with ghosts, ghouls, and possessions - things you can't kick in the nuts or poke in the eye Three Stooges style. I credit Insidious with my true horror awakening. It was the first horror movie I'd seen that scared the crud out of me, but I didn't and couldn't look away - the story was just too good. The concept of The Further - the hellish limbo where the dead sit and wait outside of time is decent nightmare fuel in and of itself, even before we are witness to the awesome imagery the movie provided.
Paranormal Activity, which brought found-footage/first person perspective back into popularity, features very little gore - relying heavily on jump scares and an over-whelming feeling of impending doom. Monstrous footprints in baby powder, sudden loud noises, and creepy sleepwalking leaves the audience sweaty and anxious without a drop of blood.
No doubt, there are plenty of horror films that rely on the shock factor that gore provides (ie: the Evil Dead remake - oh my god, the sound of that chick cutting into her face. Bravo, foley editor, bravo!).
In the end, it's all about personal preference.
Allow me to make a food analogy - horror elements are the spices of the narrative world and gore is the equivalent of hot peppers. Some people enjoy a 5-alarm dish that hurts just as much on the back end as it did upon entry. However, even the daredevil among us likes a varied menu. And hot peppers should never be included in every dish, for every occasion.