Believe it or not, one of the games that spooked me early on was Lemmings! It was smooth sailing until I hit Fun 17, and then those hidden crusher traps scared the living daylights out of me. Maybe that's why to this day I abhor traps of any kind, especially hidden ones.
I'll also give an honorable mention to King's Quest: Mask of Eternity. For anyone who's not familiar with the King's Quest saga, the final installment was a huge departure from the rest of the series. The first seven games were your typical Sierra adventure games, with convoluted puzzles that took a ridiculous amount of trial and error to solve, with many (often humorous) deaths occurring in the process.
The final game of the series switched over to the RPG genre with a few adventure-style puzzles mixed in. It also took on a much darker tone than the previous installments and added a combat element. Basically the game starts with the titular Mask of Eternity being shattered by the game's primary antagonist. This action unleashes a magical storm that turns everyone in the kingdom into stone, except for the player, who happens to catch a piece of the Mask as it falls from the sky, thus protecting him from the storm's effects. The first part of the game has the player exploring the petrified town, gathering resources and seeking clues on how to break the magical curse, while fighting hideous undead creatures that seem to pop up out of nowhere.
Once the player completes the first stage of the game in town, the environments just get more inhospitable from there. Many of the scenes in the game are very dimly lit, with background music that ranges from creepy to spine-tingling.
Many fans of the earlier games in the series were understandably upset at the darker atmosphere and combat-oriented gameplay of the final installment. Personally, I don't think the game was horrible on its own (although it had its share of bugs), but it departed far enough from its roots that it never should have been given the "King's Quest" moniker.