Kuma died of old age after Tekken 2. His son, Kuma, takes his place in later games.
King was killed by Ogre. His student became the second and current King.
Armor King was killed by Marduk in a barroom brawl. His younger brother became the second and current Armor King.
True Ogre was killed by Jin Kazama after Paul Phoenix defeated Ogre.
Kazuya was thrown into a volcano by Heihachi after Tekken 2, but was later "regenerated" by the G Corporation.
Bryan Fury was killed in a shoot-out in Hong Kong, but reanimated by Dr. Abel.
Jack has had several iterations which were destroyed then later rebuilt, upgraded, or duplicated.
Jun Kazama, contrary to popular belief, is not dead. She was attacked by Ogre prior to Tekken 3 and has been missing since.
Now that we know the current state of the Tekken universe, the first characters announced for SFxT will be featured in future editions of Know Your Tekken.
(Most of this info was obtained from Tekkenpedia.)