Agüero was born into a large family with seven children.

In 2003 he became the youngest player to debut in the Argentine First Division at 15 years and 35 days, breaking the record previously set by Diego Maradona in 1976.

Agüero's nickname "Kun", which features on his shirt, dates back to his childhood. It was first given to him by his grandparents, due to a resemblance to the character "Kum-Kum" from the anime Wanpaku Omukashi Kumu Kumu which was Agüero's favourite television programme as a child.

Agüero has a tattoo on the inside of his right arm inscribed in Tengwar - a form of writing invented by J. R. R. Tolkien in The Lord of the Rings - that transliterates roughly to Kun Agüero in the Latin script. He also has a tattoo on his left arm of his son's name and date of birth.

He caused controversy early in his Atlético Madrid career by using his hands to score the winning goal against Recreativo de Huelva in October 2006.

In 2015 Sergio Aguero scored five goals in 20 minutes in the Premier League. In a match against Newcastle he scored in the 42nd, 49th, 50th, 60th and 62nd minutes before being substituted on 66 minutes. He thus joined Andy Cole, Alan Shearer, Jermain Defoe and Dimitar Berbatov in the record books.