An Magic Archetype is a recurring deck or strategy with many possible variations.  Archetypes are defined when they have been prevalent in several tournaments and have showed results repeatedly, Top 8 or higher. They should also be an idea that is playable in many formats, rather than just a pile of cards that wins.
Archetypes are first defined when a rogue deck enters a tournament setting such as a PTQ. The deck places in the top 8, often top 4, and the list is put on the internet. People, seeing the high finish and the wacky deck design, will copy it. This is called netdecking. The deck establishes a name for itself, usually something funky, but it is not an archetype yet.
Next, people in other formats notice that the deck's unusual name and power level have really stirred things up. They decide to try the deck out in the format that they play, leading to multiple decks spread over different formats. The funny thing is, all these decks have the same name, roughly the same strategy, and often some of the same cards. Now, it has truly been transformed from a rogue deck to an archetype.
- MUC — Fatties with backup
Considered one of the strongest control-oriented archetypes, this type of deck abuses counterspells and card draw to make sure that opponent's threats never stick. It plays its own threat, usually a very large creature, such as Leviathan that it can use to bash face to end the game. Decks that fall into this archetype are Next-Level Blue, Previous-Level Blue, and Stasis.
- Aggro-Control — Weenies with backup
Also known as Fish, this deck uses control as a backup to prevent its opponent from progressing while hitting with little creatures, White weenie style. Main strategies include mana denial, Standstill and Mystic Remora type effects, removal, and bounce.
- Land Destruction — Mana Denial
Land destruction hits the opponent at its weak point — mana. Almost no deck can function without a stable mana base, and by destroying lands and artifact mana, this kind of deck wrecks the opponent's ability to even play spells. Answers require mana, and mana usually requires lands. Solution: Hit those lands. Usually Green, White, or Black based, but Red works as well.
- Discard — They can't play spells they don't have
Discard makes sure its opponent never takes control of the game by devastating his or her hand, and then keeping it that way. Discard control decks are often Black, with Blue or Green for backup. It kills with a combination of enchantments like Megrim, artifacts like The Rack, and creatures like Hypnotic Specter. Once this deck has control of the game, there is almost no comeback.
- Sligh — Hit 'em hard and fast
Full of lots of large, undercosted creatures and burn spells, sligh looks to win by sheer overwhelming beatdown at an unbearable pace. This falls under the category of tempo based decks, but only to an extent. This deck is hellbent on killing as fast as possible without using combos or expensive spells, and is seen in many different formats under many different names.
- Red-Deck Wins — Burn and beat to victory
Based almost purely on burn, this deck looks to win fast and big, by keeping threats on the board and backing them up with direct damage. Easily confused with typical sligh, RDW keeps spells like Lighting Bolt at the front line, so its powerful dudes can connect uncontested. It is named Red Deck Wins because it is fast and furious; and most notably, red.
- Storm — Play lots of spells, then finish 'em
This archetype is for a deck that wins by playing a lot of spells, to increase Storm count, and then finish with a powerful Storm effect such as Tendrils of Agony, Grapeshot, Empty the Warrens, or Brain Freeze. These decks can contain infinite combos, but are generally only worried about reaching a set goal where the spell will be lethal.
- "Infinite" Combo — Play all the combo pieces, and win
This name of this archetype is a misnomer, as there is rarely an "infinite" loop in Magic, such loops end in a tie. Instead, these decks are often made of a few combo pieces, that will guarantee either a win or the time to do so. In addition, these decks often include tutors, card draw, and enough removal to ensure that it will stay in the game long enough to combo off, and win. These decks tend to be slower, but when control elements are added, they can do very well. Examples are the Bomberman combo, and the Reveillark Combo deck.
- Reid Duke. (June 1, 2015.) "The Metagame", Daily MTG, magicthegathering.com, Wizards of the Coast.
- Jeff Cunningham. (January 27, 2007.) "Aggro, Combo, and Control", Daily MTG, magicthegathering.com, Wizards of the Coast.
- Zac Hill. (August 10, 2012.) "Ah Yes. Very Standard.", Daily MTG, magicthegathering.com, Wizards of the Coast.