Used frequently in Professional Wrestling, especially in TNA (though it occasionally shows up in WWE; listen to the Full Blooded Italians' entrance music, and you'll be reminded of "No Sleep 'Till Brooklyn" by the Beastie Boys). WCW was an even worse offender before it got bought out, which is rather odd; they were a Time Warner subsidiary, and Time Warner owned most of the labels that were getting ripped off. As noted above, this is mostly due to Jimmy Hart, the former Trope Namer himself, writing the music for these companies. Other examples include Mortis using a reworked version of the theme from The Phantom of the Opera (both characters wore a skull-like mask).
To be fair, just because they "own" the rights doesn't mean they don't have to pay the artist to use the song. It's cheaper to get JH to write the song for you. As well, Time Warner's dysfunctional structure meant that WCW (then part of Turner Broadcasting) would have to still have to go through Warner Music Group (then a Time Warner company) through the same channels as any other company.
Way before Jimmy Hart debuted in WCW, there were still JHV's; for example, Dustin Rhodes' theme before the Slam Jam album was a JHV of "Money for Nothing", and the York Foundation used a JH "Dallas" theme.
And way before that, in the JCP/NWA days, there was the JHV of Giorgio Moroder's "Chase" that The Midnight Express used.
Even more baffling than writing covers of songs they already owned, was WCW rewriting songs that were already in the public domain! Randy Savage had previously used "Pomp & Circumstances" in WWF, but it was given a rock makeover in WCW.
It sounded more like a wresting theme than somebody's graduation.
WWF did this in the early '90s when they gave Ric Flair a JHV of "Also Sprach Zarathustra".
DeGeneration-X's theme is a lyrical JHV of "Killing in the Name". The lyrics both speak of rebellion. Compare the DX theme's "We just got tired of doing what we're told what to do" to these words of RATM's song, "And now you do what they told ya," and "Fuck you I won't do what you tell me! Fuck you I won't do what you tell me!"
The same thing happened with Balls Mahoney. The Sandman, too...but not so much (it DOES bear some resemblance to "Enter Sandman", but again, not so much).
With "Enter Sandman" it was a necessity. Metallica charges $5-6 million just for the use of that one song. ECW used to have a cover version on hand just in case.
The original ECW did this too sometimes...see: Taz's music morphing from the actual "War Machine" by KISS to a JHV, to his "Survive If I Let You" theme that used the opening riff to the JH War Machine and then a completely different melody.
WWE Diva Mickie James' entrance theme is pretty obviously a suspiciously similar song of "My Sharona" by the Knack and "Mickey" by Toni Basil.
Also, Goldberg's entrance theme in WWE was a suspiciously similar song of his original WCW entrance theme (An awesome piece of stock music), due to the rights to the song not being available. The WWE version was not as awesome.
Victoria had previously used Tatu's "All the Things She Said" but was given a lyrics-less cover version for video games and DVD releases. Same goes for
The same could be said of Christian. The Waterproof Blonde version of "Just Close Your Eyes", later covered by Story of the Year and Bedlam's Gate, is itself actually the live-band-recording Jimmy Hart Composite of two of his previous themes, "At Last" (which itself—in an earlier iteration—was a suspiciously similar song of "Bohemian Rhapsody" by Queen) and "Blood Brother". Of course, one could just claim that it's a JHV of "My Last Breath" by Evanescence like his TNA theme afterwards was.
Lord help WWE if they lure Bryan Danielson in without getting the rights to "The Final Countdown".
Considering the way they're going to likely repackage him, they probably wouldn't even consider giving him something that even remotely sounds like it. Let's consider it "averted" for him...for the moment.
Apparently he actually did get a mild JHV of it in Florida Championship Wrestling, but for storyline reasons he has to use The Miz's music in WWE NXT.
Averted, as they didn't even bother JHV'ing. When he finally got his own music, at first he was using some generic-sound hard rock. And then he won the US Title, and now uses "Ride of the Valkyries". The real version. So...upgrade?
Two Steps From Hell's "Freefall", a JHV of "Freefall" called "Big Epic Thing", and then a rock version of "Ride of the Valkyries" called "Flight of the Valkyries" would follow as Daniel Bryan themes.
Ring of Honor's even started this: the music for their HDNet television show bears a remarkable resemblance to Velvet Revolver's "Slither".
Oddly enough, Ring of Honor never attempted this after the Internet outcry over Bryan Danielson having to drop "The Final Countdown". Then again, lemonade was made from this lemon, as the emotional effect when it was brought back for special "off-camera" moments, especially at his last hurrah...
A suspiciously synthesizer-heavy version was used for his entrances on Ring of Honor's TV show, however.
As it turns out, WCW using this trope has probably saved WWE a ton of headaches, as they (usually) haven't had to bother with editing music on their archived WCW broadcasts, and certainly not to the same extent as they've had to self-edit. Most of the replacement songs for WWE versions aren't even this trope in action, as they're usually not even close to the original pieces.
The Other Wiki once had an article which listed songs of which TNA composer Dale Oliver has made suspiciously similar songs. The list was rather long, but has since been removed.
That song actually was originally recorded by Hart in WCW, as the theme song for nWo 2000, but they ended up using the original "Rockhouse" instead. "Rockhouse" itself of course if a JHV of a couple Jimi Hendrix tunes...
Christian Cage's TNA theme was originally a virtual note-for-note rip of the Evanescence song "My Last Breath". It changed midway through his TNA run, perhaps for that very reason...
Angelina Love's last TNA theme, Lesson Zero, is pretty much a JHV of "Papercut" by Linkin Park, the song she still uses in the indies.
Similar to Angelina, one of Christopher Daniels' first TNA themes, which later became his ROH TV theme upon his return there in 2010, was a JHV of his ROH/indy theme, Marilyn Manson's "Disposable Teens".
Sting's original TNA theme was a poor man's "Seek and Destroy"
Percy Watson and Titus O'Neil's theme seems to be a speed-up JHV of Lil' Jon's "What You Gonna Do".
The Blue Meanie's WWE theme is a JHV of Tinman's - 18 Strings, which in itself is a JHV of Nirvana's - Smells Like Teen Spirit.
Hulk Hogan's first WCW theme, American Made, was an obvious JHV of Real American.
It also sounds a lot like Saxon's "Wheels of Steel" which might have been the original inspiration for Real American too.
The song "American Made" is on an album called Hulk Rules! by Hulk Hogan and the Wrestling Boot Band, which featured Hogan rapping. Most notable is "I Wanna Be a Hulkamaniac", which is a JHV of Owen Hart's original entrance music. The title track is a JHV of The Nasty Boys' WWE theme, sung appropriately enough by Hart himself, who did a few songs on the album.
Ted DiBiase Jr.'s "Priceless" is also a JHV, oddly enough. If you listen closely, the melody and instrumentation resemble "Money" by Pink Floyd.
The Outsiders' pre-nWo theme music in WCW was a JHV of "Crazy" by Seal.
The Wrestling Album, WWE's first album of mostly wrestlers' theme music, includes the song "Eat Your Heart Out, Rick Springfield", written and performed by Mr. Hart himself, which is suspiciously similar to Rick Springfield's song "Jessie's Girl". Justified, as it's a song about a guy who's jealous over his girlfriend's interest in Rick Springfield. Which also parallels/parodies the meaning of the original. Incidentally, the song was also used as Jimmy Hart's entrance music in the video game WWE Smackdown vs. Raw 2006.
Also on The Wrestling Album, "Hulk Hogan's Theme" is a suspiciously similar instrumental of Bonnie Tyler's "Ravishing".
Actually, Hogan's theme had predated Ravishing by a year, as it had been used in 1985 as the theme to Hulk Hogan's Rock 'n' Wrestling and on The Wrestling Album, whereas "Ravishing" had been released in 1986.
The theme to No Way Out 2001 was the JHV of Bush's "Machine Head".
Alicia Fox's old theme is a JHV of Nelly's "Hot in Herre". What makes it really funny is that the theme is called "Shake Yo Tail". Nelly also did a song called "Shake yo Tail Feather." It copies one, but was named after another, making it look like careless writing.
Kevin Nash's theme when he used the Diesel gimmick during his first run in the WWE is a JHV version of AC/DC's The Jack.
Some parts of it also sound like "Rocky Mountain Way" by Joe Walsh.
ECW's original theme song, "This Is Extreme" has its main riff similar to the main riff of White Zombie's "More Human Than Human".
Kyoko Inoue's theme that she used in AJW is a JHV of "Panama" by Van Halen which was her entrance theme for a bit in the early '90s.
Since being repackaged in 2013 as Curtis Axel, the former Michael McGillicutty now uses what sounds like a remix version of his dad's old theme, "Theme from Exodus."
Rick Rude was guilty of this three times. His first theme in WWF was a knockoff of "The Stripper". When he headed to WCW he used a knockoff of Janet Jackson's "Black Cat", and his final theme, "Simply Ravishing" was very similar to Whitney Houston's "How Will I Know" (complete with a Whitney soundalike on vocals).
The theme song that Justin Gabriel and Heath Slater used for a short period in 2011 had an opening similar to Skillet's "Awake & Alive."
Justin Gabriel's face solo theme sounds a little like the Killers' "Somebody Told Me."
And his current heel theme is a JHV of Knife Party's "Bonfire", which is a little bit silly considering WWE licensed that track for their 2K15 video game.
The debut of Ethan Carter III in TNA gave him a theme song that is a JHV of Fall Out Boy's "My Songs Know What You Did In The Dark (Light Em Up)"
Believe it or not, the nWoWolfpac's infamous rap theme song is actually a JHV of "Burn" by Militia (a little-known rap group), which the Wolfpac used as their theme at house shows.
In WWE NXT, Adam Rose's entrance theme "Break Away" by CFO$, is a pastiche of the song "World Goes Wild" by Above Envy, a song which he shortly used as his entrance theme before switching to the current one. Reportedly because WWE ended up choosing not to pay the rights for the original song.
Booker T's theme sound awfully similar to Kraftwerk's Musique Non Stop, especially when it comes to the vocals.
Sami Zayn's newest theme "Worlds Apart" has an intro that sounds very similar to "Ole" by the Bouncing Souls. Which would make sense considering what his well-known previous gimmick was.