|Penny and the Pownall Case (1948) [Jonathan Blair]: Shot to death by Ralph Michael. (Thanks to Jonathan)
Crossroads (1955) [The Ghost]: I have not seen this short film, but the IMDB's credits identify his role as a ghost.
The Dark Avenger (The Warriors) (1955) [French Patrol Captain at Tavern]: Run through with a sword at the end of a fight with Errol Flynn. (Thanks to Jonathan)
Beyond Mombasa (1956) [Gil Rossi]: Shot with a poison dart by a pygmy with a blowgun. (Thanks to Jonathan)
The Curse of Frankenstein (1957) [The Creature]: Burned to death when Peter Cushing throws a lantern at him. (Note: Although the creature was resurrected or re-created in numerous Hammer sequels, I am counting this as a death scene for Christopher since the creature was played by different actors in all the subsequent movies.)
Ill Met by Moonlight (Intelligence Service; Night Ambush) (1957) [German Officer at Dentist]: Shot to death by Dirk Bogarde. (Thanks to Jonathan)
Battle of the V-1 (Missiles from Hell; Unseen Heroes) (1958) [Brunner, Labor Camp Captain]: Strangled by Michael Rennie. (Thanks to Jonathan)
Corridors of Blood (1958) [Resurrection Joe]: Burned to death with acid by Boris Karloff. (Thanks to Jonathan)
Horror of Dracula (Dracula) (1958) [Count Dracula]: Burned to death and reduced to ash after Peter Cushing tears down the curtains to let sunlight in. (Note: Even though Dracula is always brought back in each sequel, I will still be listing these as "death" scenes.)
The Mummy (1959) [Kharis, the Mummy]: Collapses into the swamp after being shot repeatedly by police. (Thanks to Jonathan)
The Treasure of San Teresa (Hot Money Girl; Long Distance) (1959) [Jaeger]: Strangled by Eddie Constantine. (Thanks to Jonathan)
Beat Girl (Wild for Kicks) (1960) [Kenny]: Stabbed to death by Delphi Lawrence when she finds him with Gillian Hills.
The Two Faces of Dr. Jekyll (Dr. Jekyll and Mr. Hyde; House of Fright; Jekyll's Inferno) (1960) [Paul Allen]: Cushed to death by a python after Paul Massie shuts him in a room with it.
Hercules in the Haunted World (Ercole al centro della terra; Hercules vs. the Vampires) (1961) [King Lyco]: Bursts into flame when he fails to complete his human sacrifice ceremony before the end of the lunar eclipse (having been pinned beneath a stone obelisk by Reg Park).
Horror Castle (La Vergine di Noremberga; Back to the Killer; Terror Castle; The Virgin of Nuremberg) (1963) [Erich]: Burned to death after being trapped in a burning castle while trying to save his master. (Thanks to Andrea)
The Whip and the Body (La Frusta e il corpo; What; Night Is the Phantom) (1963) [Kurt Menliff]: Stabbed in the neck by Daliah Lavi behind a curtain; his body is shown again afterwards when everybody else discovers him, then again during his funeral. After his death, he appears to Daliah several times throughout the movie, but it's ambiguous whether he's a ghost or just a hallucination.
She (1965) [Billali]: Stabbed in the back with a spear by Ursula Andress when he tries to enter the Flame of Life.
The Skull (1965) [Sir Matthew Phillips]: Hit on the head with a small statue by Peter Cushing after Christopher catches Peter trying to steal the statue.
Dracula: Prince of Darkness (The Bloody Scream of Dracula; Disciple of Dracula; Revenge of Dracula) (1966) [Count Dracula]: Killed by running water when he falls into the moat, after Andrew Keir fires several shots to break the ice on the water's frozen surface.
The Oblong Box (1969) [Dr. J. Neuhart]: Throat slit with a surgical saw by Alister Williamson in Christopher's office; he dies soon afterwards, after Vincent Price discovers him.
The House That Dripped Blood (1970) [John Reid]: Burned to death (off-camera) when his daughter (Chloe Franks) throws a wax voodoo doll in the fireplace; we only hear him screaming over a shot of the doll melting.
Dracula AD 1972 (Dracula Today) (1972) [Count Dracula]: Stabbed in the heart with a silver blade by Peter Cushing. (In the prologue sequence, he was also stabbed in the heart with a wooden wheel-spoke by Peter (playing the ancestor of his present-day character), but was brought back to life shortly after the 20th-century storyline begins.) (Thanks to Garrett)
Dark Places (1973) [Dr. Mandeville]: Hit in the chest with a pick-axe by Robert Hardy.
The Man with the Golden Gun (1974) [Francisco Scaramanga]: Shot in the chest by Roger Moore at the end of a cat-and-mouse chase through Christopher's 'funhouse' hideout.
The Satanic Rites of Dracula (Count Dracula and His Vampire Bride; Dracula Is Dead and Well and Living in London) (1974) [Count Dracula]: Stabbed in the chest with a wooden stake by Peter Cushing, after falling into a pit of stakes. (Since there was no sequel to resurrect him, we can consider this to be his final "Dracula" death scene.)
Airport '77 (1977) [Martin Wallace]: Drowned (off-screen) after swimming out of the wrecked plane in a rescue attempt; his body is shown afterwards when it floats by the window and his wife (Lee Grant) looks on in horror. (Thanks to TC)
1941 (1979) [Captain Wolfgang von Kleinschmidt]: Knocked off of the deck of a submarine and into the ocean by Toshiro Mifune, after Christopher insults him. (Although the film itself implies that he was drowned, there are publicity stills from a deleted scene showing the drenched Christopher as Slim Pickens' prisoner.) (Thanks to Stephen and Uwe)
Gremlins 2: The New Batch (1990) [Dr. Catheter]: Electrocuted by a gremlin while Zach Galligan looks on helplessly. (Thanks to Neil)
The Rainbow Thief (1990) [Uncle Rudolf]: Dies (off-screen) some time after suffering a stroke; we only hear of his death when Omar Sharif learns the news.
Gormenghast (2000) [Flay]: Stabbed in the chest when Jonathan Rhys-Meyers throws a knife at him.
The Lord of the Rings: The Return of the King (2003) [Saruman]: Stabbed in the back by Brad Dourif; he then falls from the tower and is impaled on a spike. (This scene was not included in the theatrical release, but is present in the Special Edition DVD.) (Thanks to SpecialKid, Lianne, and Neil)
Crimson Rivers: Angels of the Apocalypse (Les Rivieres pourpres II: Les Anges de l'apocalypse; Crimson Rivers II) (2004) [Heinrich von Garten]: Commits suicide by shooting himself in the head. (Thanks to Gary)
Star Wars: Episode III: Revenge of the Sith (2005) [Count Dooku]: Decapitated with two light sabers by Hayden Christensen (at the urging of Ian McDiarmid), after Hayden had cut off Christopher's hands and rendered him helpless. (Thanks to JF)