Billboard described "Goodbye Stranger" as "a fluid midtempo number highlighted by the band's near falsetto vocals, dominant keyboards and a strong melody line."[5]Cash Box said it has "intriguing, well-paced vocals" from Rick Davies, and the "high backup singing" from Roger Hodgson and "blithe, spirited instrumentation."[6]Record World said that the "keyboard/guitar & chorus hook provide a blithe fairytale effect."[4]
Ultimate Classic Rock critic Nick DeRiso rated it as Supertramp's fourth-best song, calling it a "snarky kiss-off from Davies" that "showcases the band's predilection for the Wurlitzer."[7] Brett Milano of UDiscover Music rated Roger Hodgson's guitar solo at the end of the song as one of the 100 all-time greatest.[8] Gary Graff of Billboard rated "Goodbye Stranger" as Supertramp's ninth best song, saying it's "one of the best executed trade-offs between Davies and Hodgson vocals" and has one of Supertramp's "hottest guitar solos."[9]
Despite being met with only limited success in the UK, it was a major hit elsewhere, even a Top 20 hit in the United States and Canada, reaching number 15 and 6 respectively.
The song plays in many films and television programs. In the episode "Goodbye, Toby" of The Office, Michael Scott sings a parody of "Goodbye Stranger" entitled "Goodbye, Toby".[22] In the episode "Goodbye Stranger" in the eighth season of Supernatural, the song plays on the Impala's radio after the angel Castiel disappears.[23] The song plays in the trailer of the 2023 film Beau Is Afraid.[24] It is also played in the 1999 film Magnolia, and the 2017 film I, Tonya. It is featured in the second season finale of Hacks. The song is played in the first episode of the second season of the television show Reacher.