Whenever the computer is a cheating b*stard.
Copy/paste from TvTropes:
In RPGs
.. enemies have higher Level, Stat and Damage Caps than you, or can just ignore them.
... enemies can always escape from you if they run, but you can't always escape from them if you run. (Cactuar, I'm looking at you.)
... enemies have either infinite MP or spells, or so much it would take weeks for them to run out.
... the ways stats relate to each other is different for the computer.
... everything on this list goes double for bosses.
In racing games, the computer ...
... will go to their full speed instantly, especially in older racing games.
.. possesses 'rubber band' capabilities, meaning that no matter how fast you go or what obstacles you place in their path, if you are in first place then second place will always be close enough to catch you if you make even the slightest mistake.
.. has a car which has superior performance to anything you can drive.
In First Person Shooters, the computer
... doesn't have to reload, or reloads instantly (assuming you do have to reload).
... knows where movable objectives like the flags in capture-the-flag are, even if nobody on their team have seen them.
can shoot so far and so accurately that they can kill you before you can even see them.
and then some. :/