Friday The 13th - The original. I personally actually enjoy watching Parts 3 and 6 more because they're more fun, but I still prefer the original.
Halloween - Definitely the original
A Nightmare On Elm Street - The original
S aw - I never was the biggest Saw fan, but I do prefer the original over the others, though I like Part 3 as well.
Scream - The first one, all the others are almost unbearable to me (Part 2 was okay, but I hated 3 and 4)
The Texas Chainsaw Massacre - The original, I never was a fan of the more comedic route it took in the sequels
Alien - I like Aliens most, but I consider Aliens to be more of an action-thriller type movie, so if we're talking about horror series, I'd have to once again say the original.
Predator - I've never seen Predator as a horror series, but I guess I'd say the first one.
Phantasm - I've always liked Part 2 more, even though Part 1 is probably, from a critical standpoint, the better film, 2 has always been my favorite.
Evil Dead - I'm definitely in the minority for this one, but I've always liked the original more. Maybe because I always watch Evil Dead II right after The Evil Dead, but by the end of II I'm honestly a bit bored with the whole ordeal. I also always have preferred straight horror to more comedic horror.
Hellraiser - Not the biggest fan of this franchise. I like the first one, but all the others don't really do anything for me. Hellbound has its moments.
Child's Play - Once again, I like the first, definitely.
Final Destination - I don't really like this franchise all that much. I haven't seen 4 and 5 because I heard bad things about 4 so I didn't see it in theatres, and even though many fans liked 5, I skipped out on it because I was honestly tired of the whole franchise. I guess I like Part 1, though I honestly don't care enough about it to be certain.