Battle Moveset

A Good Moveset for Slowking would have to be this:

Attacks:

Surf / Psychic
Calm Mind
Rest
Ice Beam / Flamethrower / Surf / Psychic

Items Attached:

Leftovers

Preferred Nature:

Bold or Calm

Preferred Trait:

Own Tempo

Strategy Using Slowking

Calm Mind plays heavily to Slowking's strengths, Special Defence and Special Offence. As far as UU Pokémon are concerned Slowking has fantastic Special stats as well as great HP and a decent Physical Defence stat. Provided the likely counters have been moved out of the way it has a good opportunity to sweep. The main disadvantage of this set is that Slowbro, Slowking's more defensive counter-part, can perform this better due to a higher Defence stat.

EV Corner:

EVs: 148 HP / 40 Def / 252 SAtk / 68 SDef
Calm Nature (+SDef, -Atk)

A set of EVs catered to a sweeper-orientated Slowking. Should be capable of beginning to sweep after a single Calm Mind but won't be able to take many physical hits.

EVs: 148 HP / 128 Def / 56 SAtk / 176 SDef
Bold Nature (+Def, -Atk)

Tank-ish set up. A lot more durable against physical attacks but will take an extra Calm Mind to get into sweeping stats.

Other Optional Moves

Yawn, Thunder Wave, Toxic, Counter, Curse, Shadow Ball, Focus Punch, Earthquake, Psych Up. The status attacks and Counter are the only "real" options here. Yawn can work as a Pseudo-Haze move and Counter is a reasonable way to get rid of a physical attacker but suffers from Slowking having to rest off the damage. Curse is just a generally good move and if you decided to go the physical route (for surprise or novelty) it has a lot of options to back it up. Psych Up can copy another Pokémon's Calm Minds but when you have your own source of Calm Mind, why bother?

Strategy Against Slowking

First and foremost you should avoid letting it get away with Calm Minding. If you can beat it down into resting it should be easy to handle. Bug types like Pinsir and Ghost types like Banette can scare it off with the threat of a super-effective STAB. It's Physical Defence is it's lowest of the two defences. Choice Banders can take a considerable chunk out of it, just be aware that it has access to Counter, which, while uncommon on Slowking still may be present. Toxic is effective against it and will force it into an early Rest. Special walls with physical attacks (and possibly stat-ups of their own) are somewhat effective, provided you can maintain pressure against it rather than giving it a chance to set-up. Electric and Grass types are super-effective against it but the former has few options and usually has forgettable defensive stats while the former are weak to two of it's potential attacks (Flamethrower and Ice beam ) and weak to Psychic if they have Poison as a second type.

Contest Moveset

A good Contest Moveset for Slowking would have to be this for the Beauty Contest best with Modest, Mild, Rash or Quiet Nature:

Attacks:

Water Pulse
Rain Dance
Dive
Surf

Items Attached:

Blue Scarf

Strategy Using Slowking

If you do the attacks in this following order you should have very few problems; 1st - Rain Dance, 2nd - Water Pulse, 3rd - Surf/Rain Dance, 4th - Dive/Surf, 5th - Water Pulse

Locations in Games

Ruby/Sapphire/Emerald Trade from LG Colosseum/XD Trade from LG Fire Red/Leaf Green Trade from LG (FR), Evolve Slowpoke (LG)

Animé Appearences

Slowking has had a few Animé Appearence. A Movie, A Special, 2 Episodes. In the Movie, it helped Ash in finding the orbs to help stop the world from being destroyed. In the Special, we saw what it does in an average day. In the first episode, there is a Slowpoke ritual where a Slowpoke has to cross the Shellder filled lake to get hte King's Rock in order to find a place for the Slowpoke/Slowbro to live in. However all Slowpoke that try to do it have their tails bitten and become Slowbro, until one manages to get across, wears the king's rock and has its head bitten by a Shellder thus causing Slowking. In the second, it was featured as a memory from Larvitar Movie 2: The Power of One! Special 1: Slowking's Day Episode 262: A Crowning Achievement! Episode 265: Address Unown!