Well, there are two very definite contenders.
Poison headcrabs from Half-Life 2. Partly because of their horrifying death rattle, and partly because they look enough like spiders to trigger my arachnophobia. So yeah, fuck them. To be fair, I'm not a fan of arachnids or bugs of any kind in most games.

The titular Nemesis from Resident Evil 3: Nemesis. It very definitely lived up to its name, doggedly chasing you through the entire game. One of the only enemies in the series (up to 3, anyway, I've never really played much of the more recent ones) that could chase you through doors and into other rooms. The Nemesis was fast and it was relentless, and often the only warning of its arrival was the shattering of glass and a terrifying snarl of "STARS!"
