I've read a number of his short stories, as I have a habit of picking up anthologies of Victorian ghost stories. I forgot that "Carmilla" was one of his (comes of the aforementioned anthology habit, I suppose, as stories and authors get mixed up). I believe that the main influence on Stoker (and others since) was that "Carmilla" made vampires sexy for the first time, rather than being the rotting revenant of somebody's vile old woodcutter grandfather, as in most of the folk tales. Although in this case, the vampire's allure was based on understated but unmistakable lesbian sex (yes, in the nineteenth century!).
One of my favorite of his stories (or at least one of the few that I clearly remember being his) is "A Chapter in the History of a Tyrone Family," which in spite of the ponderous title is a neat little gothic thriller, which looks like something that may well have influenced Charlotte Bronte.
They dramatized his novel Uncle Silas a while back. I saw it on Masterpiece Theater so I suspect it came from the BBC. Peter O'Toole was the uncle in question, as I recall, and Jane Lapotiere (whose name I have almost certainly misspelled) was the fair heroine's rather bizarre governess, and much scenery was chewed by both of them. Anyway, I adored it, and would love to see it again.
"Green Tea" is quite good, although modern readers would be rather surprised by the main premise. I also liked "Schalken the Painter."
Poking around the internet to see what else of his I've read, some of the titles look familiar but not enough to spark off memories of the actual stories.