Building a Team

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Annoyer
An Annoyer is a Pokémon whose moveset is made to inflict non-direct damage to an opponent; by this term, I mean moves such as Toxic, Confuse Ray, Leech Seed, Will O’ Wisp etc. These Pokémon usually have good defenses as well as a decent amount of Hit Points. Consider sharing the EV’s among these three stats and having a Bold or Calm nature. Annoyers include Pokémon such as Venusaur and Crobat.
Baton Passer
A Baton Passer Pokémon, usually works best in a Baton Passing Team. Baton Pass permits Pokémon to pass on added effects to their allies such as those of Calm Mind, Cosmic Power and even Mean Look. A Baton Passer usually has one or more moves or abilities to boost his stats. The types and EV administration can vary very much, but it is generally preferred to have good Defenses and Hit Points. Umbreon and Ninjask make excellent Baton Passers.
Hazer
A Hazer is a Pokémon whose signature move is Haze. He uses Haze to counterattack Pokémon that use stat increasing moves such as Swords Dance, Cosmic Power etc. A good Speed is preferred but not necessary. A good Defense and a Decent amount of Hit Points would be wise to have just in case the opponent has already pumped himself up (especially those Baton Passing Teams). A subcategory of Hazer, the Pseudohazer, uses moves like Roar and Whirlwind to produce an effect similar to Haze by forcing a switch. Blastoise, Crobat and Vaporeon can -among other things- take up the role of the Hazer.
Healer
Healers are few but are able to counter Shufflers extremely well. They use moves such as Aromatherapy and Heal Bell to neutralize abnormal status conditions, as well as protective moves like Reflect and Light Screen. These Pokémon must be able to last long enough to support the rest of the team so boosted defenses and Hit Points would do the thing. Miltank, Blissey, Chimecho and Vileplume can all be Healers.
Physical Sweeper
A Physical Sweeper is a Pokémon made to inflict massive physical damage, the fastest way possible. These Pokémon's stats concentrate on Attack and Speed, so Adamant and Jolly natures are most suitable for them. Physical moves include Bug, Fighting, Flying, Ghost, Ground, Normal, Poison, Rock and Steel. Heracross, Tauros and even Charizard make surprisingly good Physical Sweepers.
Subpuncher
A Subpuncher makes use of the Substitute and Focus Punch Combo; since it will not be hit after using Substitute, Focus Punch will always hit. Normal and Fighting type Pokémon make a good use of this. Since Focus Punch is a Fighting move, this sub-role is categorized under the Physical Sweepers.
Rapid Spinner
A Rapid Spinner has only one purpose: counter Spikers. Rapid Spin is a move that ruins Spikes and frees the Pokémon from a continuous trapping condition (Whirlpool, Fire Spin etc). Starmie and Blastoise can both be Rapid Spinners.
Shuffler
A Shuffler has a single purpose in battle: affect all of the opponent's party with a status condition. He could be a Toxishuffler, Pyroshuffler or Parashuffler, using Toxic, Will O' Wisp or Thunder Wave respectively. After inducing the opponent with the desired status condition, it forces a switch with moves such as Whirlwind and Roar. It is best preferred to have a good Speed stat and decent Defenses in order to accompdtsh its purpose. A Timid or Jolly nature would be best for Shufflers like Butterfree and Manectric.
Spiker
Classified under the Shuffler category, the Spiker earns its name by its signature move, Spikes. Its purpose is to use three layers of Spikes along with a status inducing move and force a switch. Skarmory is the best Spiker up until now.
Special Sweeper
A Special Sweeper uses high Speed and Special Attack stats to blast its opponent with the strongest of special moves; Modest and Timid are perfect natures to pick for these Pokémon. Special moves include Dark, Dragon, Electric, Fire, Grass, Ice, Psychic and Water. Alakazam, Sceptile and Typhlosion are examples of Special Sweepers.
Sunnybeamer
A Sunnybeamer is a Pokémon that takes advantage of Sunny Day to attack with Solarbeam every turn. Many Grass and Fire types can have this moveset which is considered Special Sweeping.
Thunderdancer
This is simple; we all know the terrific combo Rain Dance and Thunder make; almost all Electric Pokémon could have this set, which is classified under the Special Sweeper category.
Staller
A Staller is a special kind of Tank that uses moves that poison, burn or paralyze. They are also called Toxistallers, Pyrostallers and Parastallers, and use either Toxic, Will O' Wisp and Thunder Wave respectively, along with protective moves such as Protect or Detect and recovery moves such as Rest. They benefit from high defenses and Hit Points, as well as items dtke Leftovers. Preferred Natures are Bold, Impish Careful and Calm. Torkoal, Dusclops and Azumarill make fine Stallers.
Tank
A Tank is a Pokémon made to last and stall time. It usually possesses high defensive stats along with a move that raises defenses such as Cosmic Power, items such as Leftovers and probably a recovery move, Rest or Recover. Preferred Natures are Bold, Impish Careful and Calm which all favor Defense or Special Defense. Torkoal and Blastoise make fine Tanks.