Professional Wrestling's entrance themes could be considered a Fourth Wall breaking version of this. Even when wrestlers change entrance music, the new music generally has a lot of similarities to the old, unless the wrestler has undergone a massive character change:
Triple H has used two different theme songs in by the band Motörhead. The group Evolution, which was led by him, used yet another Motörhead song.
The melody of "The Game" is a heavy metal version of the Rock Rap "My Time" and the instrumental "High Brain Pattern".
Some wrestlers have specific sounds at the beginning of their theme that announce their arrival, such as glass shattering for "Stone Cold" Steve Austin, the tolling of a bell for The Undertaker (even during his "Bikertaker" phase), a machinelike countdown for Chris Jericho, and the phrase "You think you know me" spoken in a woman's voice for Edge. Other examples include the car crash sound for Mick Foley and the "FEED. ME. MORE" for Ryback. These sometimes get removed after a Face-Heel Turn, since they're an obvious cue for the crowd to cheer. And sometimes a sound effect or Catch Phrase will get added to the front end of a song once a wrestler gets over.
Some wrestlers keep it regardless of their current alignment. Jeff Jarrett has had his theme start with the same wailing guitar riff for the entirety of his TNA career, Edge never lost the "you think you know me" once it stuck, and who can forget "Nature Boy" Ric Flair, whose entrances throughout his career were accompanied by Thus Spake Zarathustra, better known to many non-wrestling fans as "the theme from the 2001 movie"?
As Shawn Michaels said on an episode of Raw, while listing his various accomplishments: "I don't know if I've mentioned this lately, but I sing my own theme music!"
Commonly, when a new wrestler debuts, they're given their own generic music written by someone in-house. If they make it big, the core theme is then featured—usually as a guitar riff—when the theme is redone by a famous artist. This has happened with Chris Benoit, Kane, and Batista, among others.
Often subverted, particularly in regards to Diva Search winners. Also, WWE has a habit of recycling themes, as ECW wrestler Jack Swagger debuted on TV using Jamie Noble's old theme, then switched to "On Your Knees" by RATM tribute band Age Against The Machine once Lance Cade (who had used that theme prior) departed from the company. Another noteable re-debut, Christian, received a version of the theme he used just before departing ("Just Close Your Eyes" by Waterproof Blonde) redone by Story Of The Year.