Mine is hands down the green alien fart cloud in The Pandora Directive. For three simple reasons:

1. I don't like being chased.
2. I don't like being on a timer.
3. It scares the crap out of me to this day.

I usually panic to the point where I forget everything I need to do, despite having played the game a million times, and I spam the everloving hell out of the hint system.

Runner-up, also from the Tex Murphy series: the GRS "eyeball droid" in Under a Killing Moon. For some reason Access just felt compelled to put one pants-crapping sequence into each of these games...