There's an indelible blood stain (which probably is real), a cursed sealed chamber (which the National Trust still refuses to open) and a bunch of supposed ghosts, including one which apparently carved her name - Lillias Drummond - into the windowsill. You can see the name carved into the stone, but I'm dubious as to its ghostly origin. Still, pretty awesome. Apparently, after her death, on the wedding night of her ex-husband and his new wife they heard what they thought were tree branches scratching on the window. In the morning, her initials had appeared...! Very Wuthering Heights, I approve.
There was a Most Haunted episode made in Fyvie Castle which featured Lady Drummond, which is hilarious and you can watch it here. I experienced no such ghostly happenings. I watched another Most Haunted a while ago featuring Chillingham Castle, which is apparently officially the most haunted castle in the UK, whatever that means. There was a lot of screaming and dubious camerawork. I actually stayed in Chillingham Castle for five days or so with my family circa 2002 and... nada. Alas! I am yet to be convinced.
The creepiest thing was actually in the library, where amongst the busts of a girl, boy, man and woman, there was a death mask of a hanged murderer, complete with rope marks around the neck. It was very morbid and creepifying - as is the wont of death masks - and to make it all a bit weirder the guide in that room sidled up to us and said incredibly sinister things. He didn't blink very much and said that you should always beware your wife trying to kill you in your sleep. He definitely directed this at me, specifically. I did the polite nervous laughter thing, but honestly I'm not sure how much he was trying to be creepy and how much he just was creepy. (Where do they find these people?!)
Maybe when I'm retired I'll become a National Trust volunteer and terrify visitors. It sounds like excellent fun.