Chapter 49 of fanfiction Harry Potter & The Methods of Rationality by Less Wrong.[link]
Voldermort's evil overlord list :
Rule Twelve =
Never leave the source of your power lying around where someone else can find it.
Slytherin's monster is believed to have Salazar Slytherin's lost knowledge. After Riddle received all those lost knowledge, he killed the Slytherin's monster so nobody after him could have those lost knowledge.
Riddle killed Basilisk with an Avada Kedavra, but in my fanart he also 'Diffindo'-ed Basilisk's body afterward, just to be evil.