Battle Moveset

A Good Moveset for Nidoqueen would have to be this:

Attacks:

Ice Beam/Sludge Bomb/EQ/Shadow Ball
Thunderbolt/Flamethrower
Substitute
Focus Punch

Items Attached:

Leftovers

Preferred Nature:

Brave or Naughty

Strategy Using Nidoqueen

Bolt-Beam Sub-Punch, also known as a 'Skarm-Bliss' counter. It mostly relies on Super effectives when it comes to Bolt-Beam, since it doesn't get huge chunks of SAtk. Fortunately, coupled with Focus Punch, you have a good number of super effective hits.

Sludge Bomb or EQ could be considered over Ice Beam for STAB. It allows it to do some damage on Blissey (and the like), force it to heal itself and allow Nidoqueen a shot at getting Focus Punch in. Shadow Ball could be considered to team with Focus Punch. Flamethrower could go over Thunderbolt, since both counter Skarmory equally effectively.

Nidoqueen has a few advantages:
-Poison type negates its Ground type Grass weakness, meaning it can effectively switch into the majority of Electric types (the majority of which use Hidden Power Grass > Ice) effectively.
-Being part Ground means it can switch into Thunder Waves and being part Poison means it can switch into Toxics, which is always favourable.
-Its 4x resistance to Poison attacks means it can freely switch into Sludge Bombs (mostly received from the likes of Venusaur and Weezing, although Speed EVs are needed to block their status attacks).

It has all-round solid stats, all of which are usable, but Unfortunately it suffers from the 'Jack of all Trades, King of none' syndrome. There is nothing much it can do effectively that another Pokémon can't do better. As far as UU play is concerned, Sub-Punching isn't as effective due to the absence of Blissey. In OU play, plenty of other Pokémon can counter Skarm-Bliss better than Nidoqueen can.

Those handy at prediction should consider ditching Substitute, since Nidoqueen's Subs aren't particularly strong and they don't block many status attacks due to Nidoqueen's type combination. Any of the moves that I've suggested as replacements for Bolt-Beam would fit nicely in its place.

EV Corner:

Naughty Nature (+Atk, -SDef) - EVs: 112 Atk / 108 Def / 38 Spd / 252 SAtk

I've given it a minus Special Def nature since that's where the majority of weaknesses lie. It needs some speed if you want to be Venusaur to Leech Seed/Sleep Powder. Max SAtk Gives it a 249 SAtk stat (which isn't too shabby) while the rest of the EVs give it a solid 250 for Attack as well as 237 Def (which'll take a handful of hits). It's more favourable to ditch Substitute with this distribution, but if you can't handle the prediction factor Sub becomes a necessity.

Brave Nature (+Atk, -Spd) - EVs: 112 Atk / 146 Def / 252 SAtk

Pretty much the same thing as above, except this doesn't outrun Venusaur. Venusaur isn't exactly hugely OU, so it isn't that big a deal to not outrun it. The Def gets a bit of a beefing up on his one, though how noticeable is the different between 237 and 246 Def? Anyway, at least the Special Defence gets a small boost, meaning it'll take those HP Grasses a lot better when switching in on Electric Pokémon.

Other Optional Sets: Nidoqueen@Choice Band
Earthquake
Super Power/Focus Punch
Shadow Ball
Sludge Bomb/Rock Slide

Here's the Nidoqueen that you want to use in UU play. Unfortunately, Nidoking does the Choice Band sets much better. Anyway, Sludge Bomb isn't that good for a Choice Band set, since you want to be getting Super effectives and since SB only gets an SE on Grass types (many of which duel type with Poison and only take normal damage from it) you'll find it isn't that great. Rock Slide gets any flyers who will switch in, which is pretty valuable. Super Power's negative side effect is fine since you're in and out when using Choice Band, but for those who want an extra bit of power and know how to use it correctly, you'll want Focus Punch instead.

Nidoqueen@Leftovers
Crunch/Surf/Super Power/Focus Punch
Thunderbolt
Ice Beam
Flamethrower

It's a bit of a novelty with merely average SAtk, but Nidoqueen has a wide array of Special Attacks and the ability to use them to a reasonable level, so I gave "the all-out-special sweeper" a mention. Lack of STAB and mediocre SAtk hurts though. Crunch can be replaced by Surf or, when in OU play, one of the Fighting attacks, giving Nidoqueen a fighting chance against a Blissey/Snorlax switch in. The Salac (+Speed) or Petaya (+SAtk) berries are pretty worthless on this set. Like the Choice Bander, it needs to be in and out, capitalising on super effective hits and opportunities at free turns. It has neither the Speed or SAtk to be in play for long stretches of time.

Nidoqueen@Leftovers/Choice Band
Earthquake
Sludge Bomb
Thunderbolt
Ice Beam

Mixed sweeper and a combination of the above strategies. In and out, only this time using both offences. Sludge Bomb, Ice Beam and Thunderbolt can all be ditched for other moves since Earthquake is the core move of the set. Sacrificing Poison STAB is fine (for obvious reasons) and other special moves can replace Bolt-Beam.

Strategy Against Nidoqueen

Nidoqueen is an all-round solid Pokémon, and you can't expect to OHKO it. Even Super effective hits will usually take two turns to get the job done. Keeping this in mind, you want Pokémon that have the staying power and/or speed to take a hit from Nidoqueen. If you can catch it as it switches in it is likely to help. Choice Band/STAB Earthquakes running off of good attack stats will get the job done as well.

Contest Moveset

A good Contest Moveset for Nidoqueen would have to be this for the Tough Contest best with Impish, Lax, Relaxed or Bold Nature:

Attacks:

Endure
Take down
Rain Dance
Thunder

Items Attached:

Yellow Scarf

Strategy Using Nidoqueen

If you do the attacks in this following order you should have very few problems; 1st - Endure, 2nd - Take down, 3rd - Endure, 4th - Take down, 5th - Rain dance/Thunder

Locations in Games

Ruby/Sapphire/Emerald Trade from FR/LG Colosseum Trade from FR/LG Fire Red/Leaf Green Evolve Nidorina

Animé Appearences

Nidoqueen has had a few Animé Appearences. First Mewtwo Cloned on one New Island. Next Danny used it in his matches against Ash. After that Gary had one and used it in his battle Against Ash's Heracross & Snorlax. The rest are cameos Movie 1: Mewtwo Strikes Back! Episode 095: Navel Maneuvers! Episode 117: A Tents Situation! Special 2: Mewtwo Returns! Episode 271: The Ties That Bind! Episode 272: Can't Beat The Heat! Episode 348: The Bicker The Better!