[Eomer of the Rohirrim]

I'm slightly surprised no-one has yet mentioned my favourite scene. That would be the Hobbits escaping the Black Riders in the Shire. When they escape and reach the barge, and look back at the Rider who was chasing them. Scariest moment, I reckon. At this stage it's not about some evil guy looking to do battle and conquer the world; it's simply mysterious terror.