Television companions who died include: Katarina (companion of the First Doctor) and Sara Kingdom (companion of the First Doctor), both in "The Daleks' Master Plan"; Adric (companion of the Fourth and Fifth Doctors) in "Earthshock", Kamelion (companion of the Fifth Doctor) in "Planet of Fire", Jack Harkness (at the time companion of the Ninth Doctor) in "The Parting of the Ways", Astrid Peth (companion of the Tenth Doctor) in "Voyage of the Damned", River Song in "Forest of the Dead", Brig. Alistair Lethbridge-Stewart (as reported in "The Wedding of River Song") and Clara Oswin Oswald in "The Snowmen".
In the above list, Clara and Astrid count as both were invited to become companions and had accepted the invitation before their deaths, and the Clara who died in The Snowman is technically a different person than the Clara "no Oswin middle name" Oswald who joins the Doctor in "The Bells of Saint John". Harkness counts as being killed, but he is revived by Bad Wolf and becomes immortal thereafter; likewise River Song, though her consciousness remains active inside the CAL computer (at least as of "The Name of the Doctor". Bret Vyon "The Daleks' Master Plan" and Adelaide Brooke "The Waters of Mars" also die, but their status as actual companions is a matter of debate. In "Death of the Doctor" (Sarah Jane Adventures story), it is strongly implied that Harry Sullivan (companion of the Fourth Doctor) is now deceased, but no circumstances have been given. K-9 Mark III (introduced in the K-9 and Company spinoff movie) is destroyed in "School Reunion" but he is more properly Sarah Jane's companion, not the Doctor's. Strax is thought to have died in "A Good Man Goes to War", but is said to have been revived in "The Snowmen" (the circumstances are explained in one of the Series 7 minisodes).
Television companions in other media: Jamie McCrimmon (companion of the Second Doctor) dies in the Doctor Who Magazine comic The World Shapers. Liz Shaw (companion of the Third Doctor) is said to have died in the Virgin novel Eternity Weeps (though this is ignored/contradicted by all subsequent media, including the Sarah Jane Adventures story "Death of the Doctor", Ace (companion of the Seventh Doctor) dies in the Doctor Who Magazine comic Ground Zero, but this is again contradicted by other novels. Adam Mitchell (companion of the Ninth Doctor) dies in the IDW comic book series Prisoners in Time. K-9 Mark I (companion of the Fourth Doctor) is destroyed in the Big Finish audio drama series Gallifrey, but this contradicts the non-BBC spin-off series K9 which features this version of the tin dog (unless Gallifrey occurs after the events of the TV series from K-9's perspective).
Comic companions: Gus Goodman (companion of the Fifth Doctor).
Audio companions: Hex (companion of the Seventh Doctor), C'rizz (companion of the Eighth Doctor), Lucie Miller(companion of the Eighth Doctor), Tamsin Drew (companion of the Eighth Doctor).
Book companions: Lady Serena (companion of the Second Doctor), Grant Markham (companion of the Sixth Doctor).
Other companions have died, but then somehow been restored to life, but Harkness is the main example of this trope.