Let me start with a stroy about a few years ago - I was playing in a group that was being hunted and I thought the DM did a great job. After it was over, he told us all about it from his perspective (it started as a random encounter, so he wasn't spoiling the story at all).
The party was traveling with a caravan of performers through some terrible, magic woods. In the night, it was attacked by a pack of wolves who managed to carry off a member or two of the troupe. Unfortunate, but it all happened really fast. The woods were were in were known to be terrifying so it wasn't a shock that something like this could happen. But that was just the first night.
The next night the howling returned - loud and close. Beyond the light of the fires we could hear the movement, creatures darting in the night. The howling kept most of the party up at night and was close enough that our casters had to actually make checks in order to properly rest and regain spells.
Harassment and howling happened nightly for a week - it seemed clear that the wolves, for some reason, had targeted our caravan and were using hit and run tactics to carry off individuals. The party, and caravan was getting weaker (lack of sleep - fatigue, lack of spells regained, etc)
Despite the parties best efforts to locate the beasts during the day time, they were thwarted, but it was clear the beasts were staying close. They would leave the bodies of victims in the road ahead of the party, or otherwise displayed in some meaningless, but intentional arrangement.
This sort of stuff:
After many attacks, we managed a kill shot (a crit, the beasts would always flee quickly) and the result became clear.
The beast attacking us, along with her whelps, was not an actual wolf, but a
BarghestWhat was going on was the Barghest identified the group as a soft target with lots of people to use it's feed ability on - her family was growing quite strong and she wanted to farm us. The creatures abilities (invisibility, pass without trace, dimension door, etc) all made them incredibly difficult to track or locate and their tactics were spot on. It actually bridged 2 sessions and we were all uneasy coming back to the table knowing "it" was still out there...
So how can this help you? I think there are a few lessons for DMs:
1) The creature/person needs a PURPOSE. Creepy for creepy sake might get a few jump scares, but its not lasting and just "cheap". Something with a purpose, that is intelligent, and is coming for you, has a lot more legs in my mind. In this case, the Barghest was farming the caravan to consume and grow stronger... yikes.
2) Relevant abilities > raw power - The Barghest itself is not a dominating terror, but the DM made sure it was using its abilities, and using them well, in order to keep the jig going.
3) Give the players something to wonder about - are we being hunted? is this intentional? what is it? why? We players and our PCs all had theories as to what was going on that kept changing with each encounter.