Oh, Sabrina. You remember Sabrina, leader of Saffron City's gym: the unassuming little girl who uses Psychic-type Pokémon. At this point in the game, you haven't fought very many of those, but if you were smart, you picked up an Abra early on. By now, you should have a faithful Kadabra (or Alakazam, if your parents loved you enough to buy you a Game Boy cable. Mine didn't.) by your side, kicking the ass of Machokes left and right. Knowing this, you can probably guess that Sabrina will be tough to beat.
Pokémon is like an ultra-complex game of rock-paper-scissors. Everything is strong against something, and weak to something else. So what is Psychic weak to? Bug and Ghost. Great! I picked up this Gastly in Lavender Town. And hey, in the anime, Ash beat Sabrina with nothing but a Haunter, so all I have to do is get this thing up to level 25 and I'm set!
My ticket to victory.
Aaaand then you get to the gym and realize that something the anime neglected to mention about Haunter is that it is a dual-type Pokémon: Ghost AND Poison, which makes it horribly weak to Psychic attacks. Oh, and it only has two Ghost moves: Lick (crap) and Nightshade (double crap.) One blast from Psybeam and Haunter is KO'd before he even gets a chance to whip out his tongue. Your ass: instantly kicked.
Your many painful defeats at the Saffron City gym left you with a bitter taste in your mouth and an important lesson: the Pokémon world is set up with a system of checks and balances, but Psychic-type rules all. Better start leveling up that Blastoise.
Obviously this all changed with the "discovery" of Dark-type Pokémon in Gold and Silver. Now there are good, powerful moves that are super effective against Psychic-types, AND Dark-type Pokémon are completely immune to all Psychic attacks.
WHERE IS YOUR GOD NOW
Gold and Silver also tempered out Psychic a bit with the addition of the Steel-type, which is resistant (but not immune) to Psychic-moves, as well as the addition of pure Ghost-types and more powerful Bug moves. From Generation 2 onward, Psychic-types were demoted from terrifying demigods to impotent, sorry bastards who can be obliterated by a fucking firefly.
My problem is that I still have PSYCHIC=KILL EVERYTHING deeply ingrained into my head. I still think "Bite" is a Normal move. Then I encounter a level 16 Poochyena, and half my team is writhing on the floor in agony. I realise that the game needed to be more balanced, and that the advent of Dark and Steel also meant that Fighting-types stopped being so utterly useless, but I still remember the good old days when all I had to do was feed Rare Candy and PP Ups to my Kadabra and the Pokémon League Championship was mine for the taking.
Side note: There's a lot of talk in the Pokémon fan community about the possibility of a Light-type to counter the Dark-type. I thought it was fairly obvious that Dark-type is the counter to Psychic-type, but this would imply* that Psychic-type were somehow "good", which contradicts my assumption that Psychic-type Pokémon like Alakazam and especially Mr. Mime are inherently evil.
*Not necessarily, I suppose. It may be a case of evil versus more evil.
Links:
The Top 5 Dark Type Pokémon
Pokemon Season 1 Box Set - Indigo League
Pokemon HeartGold
Pokemon SoulSilver