Western psychic-type games like The PokeMon series feature several obvious weaknesses for these good PokeMon. The first thought that springs to mind is the darker type of attack. Since being introduced in Generation II, quick gothic moves have rendered these poor souls completely defenseless.
In brief, they are like a candle in the wind before voracious shadows. After all, bugs are the kind of odd small creature that can terrify the most powerful psychic. Anyway, it's dark-o'clock for them. Perhaps fear of the unknown, perhaps an inborn loathing for creatures who make their living by clinging to the earth.
But make no mistake: a well-timed Bug type move is formidable. And last but not least, we have the Ghost types -- yes, even Psychic types are scared of these weirdos! Such weirdo-notions do serious damage to Psychic opponents. A super-powerful Dark Pulse will thwart your Pok'mon; one little untimely Bug Bite or even that Shadow Ball?
All of these moves are super effective against a Psychic Pok'mon. But remember, a successful battle is not only just matching types and times-- it also requires skill, resourcefulness and luck.