I'm going to suggest a movie called The Mothman Prophecies.
This is not what I would call a strong "Horror" film compared to things like Hellraiser or Evil Dead. I'm recommending it because you listed The X-Files. It has a fair amount of weird random supernatural stuff going on that is centered around sighting of a "Mothman".
Loosely based on the book by John Keel which I believe was in fact a source of inspiration for many X-Files stories.
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2nd Recommendation THE FLY by David Cronenberg
This IMO is good horror has a scientist realizes his experiment has gone horribly wrong. This is Cronenberg doing "Body Horror" were the enemy is the scientist's own mutated DNA turning him into a freak monster.
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3rd The THING by John Carpenter
Possibly John Carpenter's best movie. An expedition in Antarctica finds an unearthed shape shifting alien. Enjoy the era of practical creature FX done without CGI.
[if you like this one you might also consider In The Mouth of Madness]
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4th Candyman
Something different and like Hellraiser is based on the work of Clive Barker. A reporter looks for the truth behind an urban legend in the dangerous Chicago gangland of Cabrini Green.
Ah yes, I've seen all of those except for Candyman. They were all pretty good, John Carpenter's The Thing being one of my favorite horror movies.