A lot of great responses so far, but I'll add my thoughts anyway. As
DarkKestral said, Ravenloft isn't any one core story. Every domain has a darklord, but not every story in the domain is about that darklord. And every darklord influences the "flavor" of his domain, but not every adventure in the domain has to have that flavor. This was true even in 2e. (There's a Mummy in the "Jeckyl/Hyde" domain, and a sleeping demon in the "Frankenstein" domain, just off the top of my head.)
An horror-type story arc you can imagine can fit in Ravenloft.
My personal favorite is "ordinary people discover that something is very wrong with the world (usually when that "something wrong" ruins their ordinary lives) and take up arms against the darkness." The fight may be futile (or it may not) and they may know it (or they may not), but they fight because it's the right thing to do, and even if generations of victims fall to the forces of darkness, saving even one is worthwhile. In that sense, I find it more of a true heroism than any Epic Destiny could be.
For inspiration, I look to the X-files, Buffy/Angel, and LOTR, in addition to Dracula, Friday the 13th: The Series, Dark Shadows, etc.
This works especially well when the players give you good background to draw on. Fox Mulder fought because it was personal: Aliens took his sister. Van Richten became Ravenloft's greatest hero because a vampire killed his wife and son.
As an example, in my Ravenloft campaign (Which the curious can read about at
www.themistway.com) the main PCs are:
1. A clockmaker's apprentice who fled when his mentor was killed by persons unknown
2. An half-gypsy spiritualist who, as a young boy, saw his mother killed by a spirit she was channeling
3. An herbalist, raised by her grandparents, who inherited her bard father's wanderlust and love of songs and tales of adventure
4. A miner's son, who discovered a trunk of unusual religious regalia that belonged to his mother, and found out that his parents fled a far-off land before he was born for reasons unknown
This has led to adventures revolving around those backgrounds such as:
1. Discovering his mentor's activities as a gunsmith smuggling weapons to rebels fighting a totalitarian regime (Falkovnia) which got the mentor killed. Taking up the fight again the Falkovnians to protect a town of refugees. Dealing with the amoral clockwork man his mentor built who wreaks havoc in his quest for a soul.
2. Fighting the spirit that killed his mother, which turned out to be the ghost of the vampire that killed Van Richten's family, along with the vorlog (incomplete vampire bride) that Van Richten accidentally created. Finding his long lost father and discovering that his mother bred him specifically to fight a prophecied enemy of the gypsies. (Malocchio, the Dukkar)
3. Finding that her father was embroiled in a secret society of vampires (the Kargat) loyal to the evil wizard-king Azalin Rex, and in fact has become a bardic lich in his service.
4. Finding that his mother was a priestess who fled because she found out too much about the corrupt paladin that led her faith and ruled her land (Nidala) and taking up the fight against the fallen paladin.
And just as Luke Skywalker went from farmboy to Jedi Knight, and Willow from awkward geek to kick-ass witch, the characters have grown into heroes, some with their own demons to wrestle
1. A swashbuckling gunslinger, who secretly is trying to rebuild his master's clockwork man, but with a conscience this time.
2. A powerful necoromancer, whose ever-growing spirit-powers threaten his sanity.
3. A bard who's gotten used to her influence on people getting her both into and out of trouble, now powerless against the lycanthropy she's contracted.
4. A quiet, troubled ranger, unable to trust nearly anyone after constant betrayals, more comfortable in the wilds with his wolf than with people, but dedicated to protecting the weak and powerless.
But that's just one example. Lots of other people have run successful Ravenloft campaign. Many of them have campaign journals online you can read for inspiration. Also, the 3e Ravenloft Dungeon Master's Guide gives some great advice in this area. The "weekend in hell" can be fun, but Ravenloft can be much more than that.