What is an archetype? - According to the American Heritage Dictionary, an archetype is "an original model or type after which other similar things are patterned; a prototype." In the PTCG, an archetype is a model for a deck that has been widely copied.
An archetype is not a specific card or combo of cards or even a deck. You can make a Riptide deck that uses different cards, or even a different strategy, than my Riptide deck, but the two decks are still Riptide decks.
Is an archetype the same as a Pokémon power? - No. You will notice that many of the archetypes listed below bear the name of a popular Pokémon Power, or in some cases, the name of an attack. However, there is little correlation between Pokémon Powers and attacks. Most Pokémon powers are not associated with a particular archetype. And many archetypes are not associated with a particular Pokémon Power. Some archetypes are based on particular attacks. Others, such as Haymaker, are based on strategies that don't depend on particular cards.
Can a deck use two multiple archetypes? - Yes, but only in limited cases. A few archetypes go together well or even naturally, but for the most part using two archetypes severly weakens a deck.
What are the most common archetypes in the PTCG? - It depends on what is popular. Popular archetypes fall into two classes. The first class is those that became popular because they work well. Examples of such archetypes include Rain Dance, which was the first widely popular archetype, and Riptide, the best-performing archetype at the 2001 Super Trainer Showdowns. The second class are those archetypes that counter the popular ones. For example, because Riptide relies heavily on Trainers and Feraligatr is weak to Grass, archetypes based on Trainer-denial strategies and Grass Pokémon became popular in 2002.
Does an archetype have to win tournaments to be an archetype? - No. There are many archetypes that would not do well in tournaments. Note also that the playability of certain archetypes changes as new cards are introduced and the metagame of the PTCG as a whole changes. The release of one or two sets could turns today's hot archetype into yesterday's news. Most archetypes are useful for casual play or instructing on the dynamics of the PTCG.
Beat Up - This archetype uses NG Sneasel's Beat Up attack. The player using Beat Up flips a coin for each of his Pokémon in play, including his active Sneasel. The attack does 20 damage for each head. This archetype works the same way as the classic Wigglytuff archetype, with the added benefit that if the attack does any damage at all, each Darkness Energy card attached to Sneasel provides an additional 10 damage. | Decks
Big Damage - A deck whose primary strategy is to do enormous amounts of damage in one turn. The goal is to win deciseively with a series of one-turn Knock Outs. Some archetypes are built upon the idea of Big Damage; Riptide is perhaps the most popular example. BS Charizard is a great example of a Big Damage Pokémon.
Cleaner - This archetype relies on status effects (particularly Poison and Paralysis) to draw a few prizes while building a big hitter on the bench. Arcanine is popular with these decks.
Conductivity - This archetype uses Dark Ampharos's Conductivity power. The Conductivity power does 10 damage to an opponent's Pokémon whenever he/she attaches an Energy card from his or her hand to that Pokémon. | Decks
Crobat - This archetype uses NR Crobat as a primary attacker.
Deep Sleep - This archetype uses Dark Gengar's Deep Sleep power. The Deep Sleep power requres the player of an Asleep Pokémon to flip two coins to wake it up rather than just one. If either coin is tails, the Pokémon is still Asleep. These decks make use of Pokémon attacks that put the Defender to sleep, in the hopes that its player will be unable to wake it up again to attack. | Decks
Damage Swap - Damage Swap decks use Alakazam's Damage Swap power to move damage between the Active Pokémon and the Pokémon on the bench. Damage Swap decks generally fall into two groups: defensive Stall decks and offensive attack decks that use cards like Sabrina's Golduck. | Decks
Erika's Jigglypuff - These decks are based on Erika's Jigglypuff L13, whose Group Therapy attack removes damage from all Pokémon and Pulled Punch attack does 40 damage if the defender has no damage counters on it.
Fire Recharge - These decks use Typhlosion L55's Fire Recharge power to feed Fire Energies to big Fire Pokémon such as BS Charizard or Blaine's Arcanine. This ability makes those cards, which usually discard Fire Energies, more playable. | Decks
Haymaker - Haymaker decks are designed to inflict heavy damage quickly. They feature Pokémon that can do a moderate amount of damage for a relatively low energy cost. These decks use only Basic Pokémon and generally do not make use of Pokémon Powers. | Decks
No Evolutions - These decks use F Aerodactyl, whose Pokémon Power allows no more Evolution cards to be played. These decks are similar to Haymakers but focus on putting the opponent at a competitive disadvantage rather than on winning quickly.
Psylink - These decks combo Sabrina's Alakazam with other Psychic Pokémon. Sabrina's Alakazam's Psylink power gives it the ability to use attacks from any other Psychic Pokémon that you have in play.
Rain Dance - A Rain Dance deck uses Blastoise's Rain Dance power. This power allows you to attach multiple Water Energies to your Pokémon in play in each turn. Rain Dance decks feature Water Pokémon with powerful Water attacks. | Decks
Riptide - This deck focuses on Feraligatr L69's Riptide attack, which does damage based on the amount of Water Energy in the discard pile. This archetype won 4 of the 6 top positions at the ECSTS 2001. | Decks
Sneasel - See Beat Up.
Stall - Stall decks are designed to prevent the opponent from inflicting damage and to force the opponent to draw all the cards from his deck. They usually feature minimal amounts of Energy, lots of Trainers that can remove damage, and Pokémon with high HPs. With the rise of heavy-damage archetypes and good recycling strategies, Stall is not very effective these days. | Decks
Shapeshift - These decks are based on Brock's Ninetales. This card's power, Shapeshift, allows you to attach an Evolution card from your hand to Brock's Ninetales, and treat Brock's Ninetales as if it were that Pokémon instead. These decks often use several different Evolution cards without the lower stages, using Brock's Ninetales to "evolve" the Pokémon instead.
Steel Pokémon - The main attacker in this archetype is a strong Pokémon with a high-energy attack that does significant damage not only to the Defending Pokémon but also to itself. Each Metal Energy card attached to the Pokémon reduces the damage done to self by 20 while reducing the damage done to the Defender by only 10. Steel Chansey (based on BS Chansey's Double-Edge attack) is the first widely-popular variant of this archetype. Other variants include Steel Arcanine (based on BS Arcanine) and Steel Rocket's Zapdos. | Decks
Trainer Denial (aka Lock) - These decks use Dark Vileplume, Slowking, or other strategies to prevent the opponent from using Trainer cards. Since many of the popular archetypes rely heavily on Trainer play, these decks have become popular. | Decks
Trample - These decks focus on ND Tyranitar. Tyranitar's Trample attack does at least 50 damage to the Defending Pokémon and possibly 30 damage to each Benched Pokémon. These decks often use Unown [D] to prevent the damage done to one's own Pokémon. | Decks
Wigglytuff or Wave - This archetype is based on J Wigglytuff's Do the Wave attack. This attack does 10 damage for each Pokémon on your bench. Naturally, these decks use lots of Basic Pokémon and Trainers such as Pokémon March to fill the bench. | Decks
Thanks to Dan the Pokeman for providing information for this article.