Those whose deaths have been shown or mentioned in the show are: Katarina, Bret Vyon & his sister Sara Kingdom, Adric, Kamelion (a robot, so may be considered to have been destroyed, rather to have died), Harry Sullivan (spoken of in the past tense by Sarah Jane Smith in "Death of the Doctor", implying that he had died), Astrid Peth, Adelaide Brooke, River Song, Abigail Pettigrew, Alistair Gordon Lethbridge-Stewart (death reported to the Doctor in a telephone call in "The Wedding of River Song"), Amy Pond & her husband Rory Williams (deaths not shown but implied by their gravestone in New York) & Clara Oswin Oswald (who seems to be able to return from the dead or to be reincarnated in some manner not yet revealed). Jack Harkness has died & returned to life many, many times.
Note that some of these may or may not be considered companions, depending on the definition of "companion".
Because the Doctor & some others can travel in time, it is quite possible for a character to appear, alive, after his/her death has been shown or reported (River Song is the most obvious example of this). The Doctor may travel to a point in time after a character's death, then return to a point in time during that character's life. By the time of the main events of "Utopia", which took place near the end of the universe, almost all former companions would have been dead.
Finally, several former companions may have died in the Time War but we have not been given clear information about this.