Resident Evil: Code Veronica X for PS2.
It was in the early beginning of the game around the area I'm supposed to be captive. It was after you find the first green herb (an item that heals your wounds) near by the stairs to a house. Then there was a small path, to the left was a wall, with some windows.
I was pretty scared to begin with because I still had no gun. So I was kinda "Oh noes, there are zombies, I better go back". So I turned around, went a few steps when suddenly one of these windows crashed and the zombie dogs came after me. I was terribly in shock and I haven't played this game since then, that's about 5 years.
(EDIT: LOOOL, Marzy beat me to it xDDD)
The moment when I had the most panic was in Zelda, Ocarina of Time with the Wallmasters and Redeads and many can relate to this.
Also, the Angry Sun from Super Mario Bros. 3 and Phanto from the second one were pretty scary, and the Grim Reaper in Kid Icarus too. I've got childhood traumas thanks to Nintendo xD