Jack Harkness in his "World War II" coat. (TV: Fragments)
Jack Harkness wore a grey greatcoat which was described by Gwen Cooper as "one of those big sort of military coats." (TV: Everything Changes) Upon seeing Jack in his coat, Martha Jones described it as "like World War II." (TV: Utopia) Indeed, Rex Matheson would give Jack the nickname "World War II" due to his attire. (TV: Rendition et al.) A hat check boy termed the coat as "vintage". (TV: The Middle Men)
It was because of Jack's coat that Owen Harper believed him to be "gay", clarifying his view that "period military is not the dress code of a straight man." Gwen thought that it suited him and was "sort of classic". Toshiko Sato concurred with Gwen. (TV: Day One) Ianto Jones was also fond of it; in his first and second encounter with Jack, Ianto respectively commented that he "love[d]" and "really like[d]" the coat. Offering dry cleaning among other services at Torchwood Three, Ianto Jones reasoned that Jack's coat "must take a battering." (TV: Fragments) Putting his coat back on following the temporary destruction of his body, Jack was told by Ianto that he had missed it. (TV: Children of Earth: Day Three)
The coat proved to be a distinguishing accessory for Jack; both Mark Lynch (TV: Combat) and Rhys Williams identified him by his coat. (TV: Meat)
In order to assist Captain Jack Harkness, who had taken his clothing and acted as the Doctor to finish his work as he recovered from regenerative collapse, the Sixth Doctor took his coat and in turn pretended to be Jack. After their work was done, the Doctor hesitated in returning the coat to Jack, finding that he had "[cut] a dash" in it, he claimed to reason that such coats would not be hard to come by. Jack, however, insisted that he exchange the coat for his own, claiming that he would have only put cat badges on it. (AUDIO: Piece of Mind)
Jack offered Brad a button from his coat after having sex with him. Brad told Jack not to damage his coat, adding that he would jump over his bar to protect it. He clarified to Jack that he liked the coat "passionately". (TV: Dead of Night)
A hat check boy told Jack that he loved his coat, to which Jack responded by suggesting that "the three of [them]" have a drink sometime, "you, me, and the coat." (TV: The Middle Men)