First Founding

After he conquered Terra, the Emperor of Mankind set out on a Great Crusade to re-unite the lost human colonies into a mighty Imperium. He soon realized that bog-standard humans wouldn't be enough; some situations called for a small number of devastatingly powerful warriors, a surgical strike force to smash enemy linchpins. To fill this role, he created his Primarchs, and from their genes, he created the Legiones Astartes, the twenty Space Marine Legions:

Legion Number	Primarch	Homeworld	Name of the Legion	Allegiance
I	Lion El'Jonson	Caliban	Dark Angels	Loyal
II	+++Records expunged+++
III	Fulgrim	Chemos	Emperor's Children	Traitor
IV	Perturabo	Olympia	Iron Warriors	Traitor
V	Jaghatai Khan	Mundus Planus	White Scars	Loyal
VI	Leman Russ	Fenris	Space Wolves	Loyal
VII	Rogal Dorn	Terra	Imperial Fists	Loyal
VIII	Konrad Curze	Nostramo	Night Lords	Traitor
IX	Sanguinius	Baal	Blood Angels	Loyal
X	Ferrus Manus	Medusa	Iron Hands	Loyal
XI	+++Records expunged+++
XII	Angron	Unknown	World Eaters	Traitor
XIII	Roboute Guilliman	Macragge	Ultramarines	Loyal
XIV	Mortarion	Barbarus	Death Guard	Traitor
XV	Magnus the Red	Prospero	Thousand Sons	Traitor
XVI	Horus	Cthonia	Luna Wolves/Sons of Horus	Traitor
XVII	Lorgar	Colchis	Word Bearers	Traitor
XVIII	Vulkan	Nocturne	Salamanders	Loyal
XIX	Corax	Deliverance	Raven Guard	Loyal
XX	Alpharius Omegon	Unknown	Alpha Legion	It's complicated

Horus Heresy

For all their power, the Space Marines and Primarchs were not perfect; half of them were sufficiently flawed to be tempted by (or driven to) Chaos, led by Warmaster Horus. The traitors were defeated, but at a terrible cost, including the near-death of the God-Emperor of Mankind and trillions of deaths.

Roboute Guilliman decided that the so-called Horus Heresy was proof that one man could not be trusted with power over one-twentieth of the Imperial Armed Forces, so he enacted several reforms to divide the Imperial Army into the Imperial Guard and Navy, and split the remaining loyalist Legions into Chapters, in accordance with his Codex Astartes. This event was later known as the Second Founding.

Two Unknown Legions

In the First Edition of Warhammer 40,000, the twenty First Founding Chapters were all known. It seems that Games Workshop had more love for some than others; when they made fluff revisions in the transition to Second Edition, the Valedictors and Rainbow Warriors were demoted to one of the "Later Foundings."

Nowadays, nothing concrete is known about the Legions II and XI, and likewise their unknown Primarchs. It is suggested that the Space Wolves destroyed them for some reason, and in the Horus Heresy book The First Heretic, a daemon suggests to the Word Bearers that the eleventh Legion in particular did something really bad, and that the left-over Marines were folded into the Ultramarines.