A crazy-strong battler in the Gameboy days due to being strong in every stat that matters, alongside the high Speed. Tauros had the strongest Hyper Beam in the game, and would down anything that wasn't a Rock-type to be KO'd in one hit. The coverage with Earthquake and Blizzard only bolsters Tauros, and its Critical Hit hax was insane. Cloyster is the only reliable switch-in, as it has enough Defense to sponge a Hyper Beam, and resists Blizzard. Articuno does okay too.
Basically a slightly weaker but slightly faster Tauros. Just paralyze it or send in a Cloyster, and you're fine.
The only Pokemon to do super-effective damage was Gengar, and that was just with Lick. It could hit back with Psychic, and boom, dead Gengar. Alakazam has immense special strength and eually impressive Speed, maining lots of Critical Hits. The only good counter to an Alakazam is another Psychic-type like Alakazam or Hypno, or a Gengar, crossing your fingers that you can attack first. Bulky Pokemon like Chansey or Snorlax also work wonders.
Zapdos is really only good to switch in and attack in bursts, but STAB Drill Peck / Thunder results in a powerful hit, coming form this bird. An immunity to Earthquake lets it safely switch in on big threats. Rhydon, Golem, and Onix all counter Zapdos fairly well, or other Electric-types such as Raichu.
A great typing that allows for really powerful sets; it's basically an alternate Alakazam. Thunderbolt and Mega Drain, and even Explosion! Hypnosis is a nice addition that Alkazam wishes it could have. It's rather frail though, so a sturdy Rock-type like Rhydon could OHKO with Earthquake as long as there's no Mega Drain, but Alkazam is the no-fail counter.
Mainly used for its Speed, Special, and access to Bolt-Beam. Starmie is certainly one of the stars of OU in Gen 1. Recover and Thunder Wave fit it like a glove, as it can slow down threats like Alakazam, which makes it easy to force switches on dedicated Psychic-types. Use an Electric-type like Zapdos or Raichu to stir up some stuff. Exeggutor works really well too.
Every Pokemon in OU back in Gen 1 is a threat, but these are the biggest ones. Maybe others will mention additional threats. :)