Some obvious picks, but good ones (the two
Frankensteins, Dawn of the Dead, Aliens, ED2, Gremlins 2).
Scream 2 is perhaps debatable, I know quite a few who would choose one of the other Craven sequels, e.g.
New Nightmare (edit: oh doh, that's not a
first sequel). I haven't seen the last three picks.
Texas Chainsaw Massacre 2 also has a following. I guess I respect the conceit (making the "subtext" of the original very explicit), though I have to admit I still find the film mostly just unpleasant.
Fulci's
Zombie Flesh Eaters is also known as Zombi 2, an off-brand sequel to Dawn of the Dead.
There's also his unofficial Gates of Hell trilogy, where
The Beyond (arguably his best and most famous film) being the sequel to
City of the Living Dead. Of course, you have Carpenter's unofficial Apocalypse Trilogy, where
Prince of Darkness is the first sequel to
The Thing.
The Pit and the Pendulum followed the
House of Usher in Corman's Poe Cycle, so I guess that counts. Good fun.
... and some have argued
The Testament of Dr. Mabuse is a horror film...