The eponymous hero of Sophocles' Ajax goes on a murdering rampage of sheep and cattle after Athena strikes him with madness. It's pretty clear that he was intending a rampage against Odysseus and the Greek troops anyways, but it would have been slightly less humiliating.
Jonathan Brewster in Arsenic and Old Lace is indicated to be a prolific Serial Killer with a love of torture, and it's clear that he's been this way since he was a child, since his hobby then was torturing his brother by putting needles under his fingernails. He's murdered as many people as his two aunts combined, but did it far less calmly. He wants to kill again just so he can be ahead in the count.