Method: Crushing by Elephant
Deadly Debut: India, 4,000 years ago. (It’s probably older, but recorded history doesn’t go back that far.)

A wood engraving of an execution by elephant published
in the 1868 issue of Le Tour Du Monde. (Image Credit: Wikipedia)
Method: Crucifixion
Deadly Debut: Nobody knows for sure. Somewhere in the Middle East, probably in the 7th century B.C.E.

"Crux simplex", a simple wooden torture stake, according De Cruce Libri Tres by Justus Lipsius (1547-1606) (Image Credit: Wikipedia)
Method: The Brazen Bull
Deadly Debut: Siciliy, during the tryannical reign of Phalaris (570 - 554 B.C.E.)

Method: Ling Chi
Deadly Debut: China, around the beginning of the Song Dynasty (10th century C.E.)

[Note: Image from a film by Taiwanese artist Chen Chiej-jen called Lingchi - Echoes of a Historical Photograph, interesting article in Taipei Times (warning: gruesome images)]
Method: Cave of Roses
Deadly Debut: Sweden, during the Middle Ages (circa the 13th century C.E.)
Method: Keelhauling
Deadly Debut: Holland, 1560 (when it became part of Dutch naval laws, though it was probably used earlier)

Keelhauling (Image Credit: Everyday Life in Tudor Times)
Method: Spanish Donkey (or Wooden Horse)
Deadly Debut: Spain, 17th century

Wooden horse (Image Credit: The Salacious Historian’s Lair)
Method: Guillotine
Deadly Debut: France, 1792

Executioner assistants dismantling the guillotine inside the Santé prison after the execution of French mass-murderer Marcel Petiot in 1946 (Image Credit: The Guillotine Headquarters)
source: neatorama.com