The weirdest glitch I've ever encountered in a video game happened in a Bethesda game; which is perhaps only appropriate.
I was playing Oblivion, adventuring with my Nord warrior on the eastern reaches of the map, searching for the ingredients for a vampire cure and Ayleid statues. I descended into an Ayleid ruin, knowing a statue was hidden there, and encountered a dread zombie.
Now, zombies are quite hard hitters in Oblibion, so I wasn't surprised when I was staggered by his lunging attack. So I prepared to recover and strike back, when the zombie hits me again, and staggers me again. And again. And again. I watched helplessly as I died without being unable to move or strike back at all. Reloading, I wondered why this had suddenly happened. Perhaps the zombies here were stronger than usual? Perhaps vampirism had given me an unmentioned weakness to staggering?
I resolved to avoid this problem by striking first with my two-hander, and keeping out of range. This time, the zombie went down easily, because my attacks seemed to have inherited the same powers as the zombie: all my hits caused a stagger.
But this was only the tip of the iceberg of strangeness. Every monster in the dungeon was a zombie, and every chest even the boss chest, only contained exactly 89 gold.
I began to realise that something had happened to the RNG; the whole 'randomness' thing had disappeared. Dungeons would only generate a single type of monster, chests would only contain a single sort of loot, and effects like staggering would occur 100% of the time. To this day I have no idea what caused it.