Awesome in UU, as he sops up some special attacks nicely, and gets some neat moves (Thunder Wave and Counter come to mind). He won't really get anywhere in OU, though; Slowbro is generally superior there.
Switch in on some other Water, or a Fire-type, and start with paralyzing your counter. Then start Calm Minding and whooping away your opponent. Slowbro does this better because the defenses are switched, but Slowking isn't bad at this. Ice Beam is mostly for OU use, because in UU, Flamethrower hits all the Grass Pokémon just as hard, and also hits Pinsir, who is far more common than Fearow. If BLs are allowed, Flamethrower also hits Scizor 4x effective and hits Lapras for neutral damage instead of 1/4 damage. Psychic is good for hitting other Waters, Heracross, and nailing most Grass-types super effective on their second type, Poison.
If you can't predict, use Substitute, but usually you should see Blissey or Snorlax coming from far away to Focus Punch them in the face. Thunder Wave can prove very useful, but watch out for incoming Heracross and other Pokémon with guts.
Slowking is much better than Slowbro at Cursing, due to his higher Special Defense, but without a STAB move, he still has trouble hurting anything. This set can pull off a nice sweep lategame, but the Calm Mind set is usually better.
Counter works first on sheer surprise, and then makes them more careful about hitting you after that. If you combine it with Calm Mind, special attacks won't do much, and the opponent will be afraid to hit it with a physical attack due to Counter. Yawn forces switches, so it's cool with Spikes and / or Focus Punch. Plus, you could switch to a Belly Drummer or some other sweeper after Yawn: if they stay in, they fall Asleep and you get a free turn. The Fire moves can OHKO Scizor / Forretress and are an alternative to Ice Beam for dealing with Grassers.
Slowking usually needs max HP because he will be taking both physical and special attacks. Optionally, you could go with 16 Speed EVs, that way you outrun anything you paralyze.
Set #1 (Calm Mind) needs a lot of Defense to make Calm Mind work, the leftover EVs in Special Attack.
A must in set #2 (Focus Punch) is to have at least 210 Attack (stat) to dent Blissey. Anything you have left is for Special Attack.
Set #3 (Curse) obviously has a lot of Attack and Special Defense, the opposite of set #1.
Checks and Counters
Depends highly on the set, there is no 100% counter. Snorlax is the safest bet. Raikou, Zapdos, Jolteon, Blissey, Regice, Swampert, Gyarados, Celebi, Vaporeon, Porygon2, Heracross, and Venusaur can work. In UU, Electabuzz, Lanturn, Meganium, Pinsir, Quagsire and Manectric. While nothing is a complete stop to all sets, Slowking won't have as much of an impact with his surprises as something like Gengar or Alakazam.