For as long as film has existed, so have sequels. There are an unavoidable delight. Many do not always enjoy sequels, but I love them. I think seeing the continuing existence of characters is one of life's many joys. Many sequels, unfortunately, do not live up to the thing(s) that came before, but here are some I think do. This list will only contain direct continuations with the same characters.
1. Evil Dead II
A lot of people still think that this is actually a remake, but I assure you, it's a sequel. Picking up very shortly after the events of the first film, with a little right-issue educed retconing, Evil Dead II is a testament to the fact that horror and comedy compliment each other extremely well.
2. Child's Play 2
With less scares and more fun, Child's Play 2 is the best sequel from the franchise. It might not be as great as the first film (and the exclusion of Chris Sarandon is a little sad), but with Brad Dourif returning to the part, you can be sure it's just as exciting.
3. Friday the 13th: The Final Chapter
While far from being "The Final Chapter", the fourth Friday the 13th film will always be my favorite. Be it my extreme dedication to Corey Feldman or sheer delight at Jason Voorhees meeting his overdue, albeit short, death. But as they say, you can't keep a good guy down...I think I should have used that line for #2, as that's a direct quote...or was that in Child's Play 3?
4. The Omen 2: Damien
The Omen is probably one of the greatest horror movies ever. It's certainly one of my favorites. But the sequels will always hold a special place in my heart. The growth of the character Damien Thorn is extremely well chronicled. The thing I love most about 2 is that so many people are in on it. The fact that Damien is the anti-chirst isn't even a secret. The thought that so many people in his life are willing to help him achieve his destiny is extremely scary. Also, The Final Conflict is great and if you really want to continue, there are novels out there for The Omen IV: Armageddon 2000 and The Omen V: The Abomination.
5. Fright Night Part II
The end of Fright Night certainly sets up for a sequel. What we get is completely different, but in a good way. Charlie is now in college and Peter Vincent in back to hosting Fright Night. The subtle humor of the first film is replaced with overt comedy, but balanced with a good story and excellent characters. The DVD is Out of Print and no one is honestly sure who own the rights to this film. Seek it out if you can, I highly recommend it.
6. Halloween II
Continuing mere seconds after the first film, Michael Myers is out to finish what he started and find his sister at all costs. With the return of the entire original cast (where necessary) and a script from John Carpenter and Debra Hill, Halloween II is the best companion piece the original could ask for. Those two as a double feature is enough to make anyone afraid of the boogeyman.
7. Jaws 2
There will be debate forever as to if Jaws is a horror movie or not. I think it's a monster movie of sorts and deserves a home in the horror movie genre. Jaws 2 is a fun ride for anyone who loved the first film. It won't blow you away, but it will make you even more scared to go into the water. Because apparently sharks hold grudges.
8. Warlock: The Armageddon
Warlock is one of my favorite "horror" movies (It's not really horror, it feels more Sci-Fi-ish). It's clever, fun and greatly cast. Julian Sands is the only character to return for the sequel and even that seems to give it too much credit. This is one of those "So Bad, It's Good" movies. It's certainly worth the watch if you enjoyed the first one.
9. Poltergeist II
The entire Poltergeist Trilogy is a neatly contained film series (Aside from the obvious "In case we want another one" end to 3). You can watch them all in sequence and it it flows incredibly well. II is my favorite of the franchise, as the inclusion of the character Reverend Kane makes it the perfect creepy ghost story.
10. Psycho II
Psycho did not need a sequel. It was completely unnecessary and absurd that someone even decided to make it. But I could not be happier that they did. The continued story of Norman Bates is one that is really worth telling. Even Robert Bloch thought so, as he wrote a Psycho II novel that is very different from the film we received. In addition to II, Universal also made a third and fourth film for the series. Norman Bates might not have the slasher chops like Freddy or Jason, but his story is certainly more interesting.
Hopefully there are a few sequels in there that you haven't seen. It's always good to be surprised that something has a sequel.
Stay tuned, as the next installment will be horror sequels that either share the name of the film before but aren't really related or are related, but do not share the name or any characters!