The Monster Of Specter Island is an In-Universe example. It's described as being a cross between a bear and a gorilla and is very vicious and territorial. It's first reaction is to chase Danny and Star across the island and attack them. While Danny could easily handle a ghost like it with his powers, he was still suffering the effects of the anti-ghost algae that rendered him without his powers. So, he and Star had to rely on each other in order to survive. While they manage to survive the experience, it is rather terrifying from Star's point of view.
After getting trapped inside the school by accident, Danny and Star's attempts to get out and contact help fall flat. At first, it's believed to be coincidence and misfortune, until Danny realizes that someone is deliberately trying to sabotage them. In other words, they are trapped at school at night, their families have no idea where they are and they are being stalked by someone with malicious intent.
From Star's point of view, getting lost in the Ghost Zone counts.
Sam and Star get stuck together at Camp Skull and Crossbones, an abandoned campsite. As if that is not bad enough, there is something lurking on the campgrounds, stalking them. Turns out it was Wulf, who was trying to help them but they panicked and assumed the worse. It's still rather unnerving in hindsight.
Dani's entire situation about being stalked and chased by an elusive ghost hunting robot is definitely worth mentioning.