|The Last Valley (1970) [Korski]: Stabbed in the stomach with his own spiked helmet by Michael Caine. (Thanks to Gordon)
I, Claudius (1976) [Augustus]: Poisoned after Sian Phillips coats the figs in his garden with poison; he dies after a prolonged period, while Sian talks to him on his deathbed.
The Story of David (1976) [Abner]: Stabbed to death by Norman Rodway. (Thanks to Gordon)
Blake's 7: Cygnus Alpha (1978) [Vargas]: Explodes in the vacuum of space after Sally Knyvette transports him there with the teleporter. (Thanks to PortsGuy)
The Black Adder: The Black Seal (1983) [King Richard IV]: Poisoned, along with the rest of the royal court, when they all drink a toast with poisoned wine.
Robin Hood: Prince of Thieves (1991) [Lord Locksley]: Killed (off-screen) by Alan Rickman and Alan's men; his body is shown afterwards when his son (Kevin Costner) discovers him hanging from a parapet. (Thanks to Jennie and Leslie)
Hamlet (1996) [Ghost]: Poisoned (off-screen) when Derek Jacobi pours poison into his ear as he sleeps; he appears as a ghost to his son (Kenneth Branagh).
King Lear (1999) [King Lear]: Dies of old age, compounded by heartbreak over the death of his daughter (Phillipa Peak). (I haven't seen this version, but I'm familiar with the story.)
Tarzan (1999; animated) [Mr. Clayton, the Gorilla Hunter]: Hanged/strangled by vines after he gets tangled in them in the jungle, as he unsuccessfully tries to cut himself free. (Thanks to Drew)