The Lexicanum article on the Primarchs
[link] lists the fate of each one, but to summarise:
• Lion
El'Jonson was almost killed by Luther in a psychic attack, but has recovered and is chilling inside the Rock.
• Dorn was killed during a boarding action in one of the first Black Crusades. His body was recovered, and his skeleton is kept in stasis. Supposedly, later chapter masters took to graffitiing his finger bones.
• Kurze/Night Haunter supposedly allowed himself to be killed by a Callidus assassin, although the vid-feed cut out just before the assassin struck.
• Sanguinius was slain by Horus during the attack on Horus's battle barge.
• Ferrus Manus was decapitated by Fulgrim on Isstvan V, during the Drop Site Massacre.
• Guilliman was dealt a mortal blow by Fulgrim some time after the Heresy, and his body locked in stasis. However, the neck-wound shows slow signs of healing, even within the stasis field.
• Horus was taken out by the Emperor at the climax of the Heresy.
• Alpharius or Omegon (or perhaps neither) was killed in single combat by Guilliman after the Heresy.
Fulgrim, Perturabo, Angron, Mortarion, Magnus the Red and Lorgar are all now Daemon Princes, hanging around in the Eye of Terror. Khan disappeared into the Webway hunting Dark Eldar, and Russ, Vulkan and Corax were each last seen entering the Eye, with Russ and Vulkan proclaiming that they would eventually return. They haven't yet.