The moments I have screamed in fear have always been when a message similar to this appears on the screen:
"The data in save file 1 has been corrupted. Retry?"
EDIT: After thinking about this for a while I realised there actually was a game where I seriously got scared, probably because I was so young at the time. My skin would just crawl when I could hear the dragon breathing in "Advanced Dungeons and Dragons" for the Intellivision.







