It was a poisonous asp, a Cobra or a horned viper. However, it is also speculated that Cleopatra may have killed herself with a hairpin dipped in poison!
"Asp" is an ancient term used to refer to a venomous snake. The most common venomous snake of Cleopatra's time and the one that is likely to have killed her, if indeed she was killed by a snake was the Egyptian cobra.
Cleopatra tested various poisons on convicted criminals to see which was the most effective for execution of criminals who were deemed worthy of a more dignified death. She concluded that the venom of the asp was the least painful and effective, causing sleepiness without spasms.
Cleopatra is also rumored to have died of an overdose of opium and hemlock, but this story is less known than the snake account.