It’s only natural to celebrate the music world’s towering achievements. The greatest albums ever released? Let’s have a list. The most thrilling tours and collaborations the world has ever seen? It’s time for a countdown. The most exciting singles in the history of human endeavour? Sounds great – let’s have a multi-page, gallery-style roundup that looks as if it won’t have Bohemian Rhapsody in the Top 3 but always does. But what about the best pop moments the world has never seen? The songs that were never recorded, the ideas that were never realised, or the meetings of minds whose minutes amount to no more than a list of apologies for absence? At the time of writing, Sia’s song Cheap Thrills is heading to No 1. It was originally written for Rihanna, and along with the rest of Sia’s current album This Is Acting, which consists entirely of songs rejected by other artists, Cheap Thrills is a portal to a parallel pop dimension where every “no” in pop history is a “yes”, where every fiasco of a recording session is a roaring success, where record labels throw caution to the wind and where Rihanna sometimes says yes to a perky toe-tapper.

Sia. Photograph: PR company handout

1 Cheap Thrills is just the start of Sia’s recent run of bad luck with Rihanna: This Is Acting contains another three songs Rihanna knocked back during the Anti sessions. Other tracks submitted for Anti include Grimes’ Go and Major Lazer’s Lean On. Rihanna may not lose much sleep over the former; the latter went on to become the most streamed song of all time. Previously Jessie J’s debut single Do It Like A Dude and Miley Cyrus’s We Can’t Stop had also been pitched to Rihanna, thus providing the ultimate philosophical question: would it be fair to force Rihanna to record all songs sent her way, if only to erase Jessie J from existence?

2 Beck’s late-90s attempt to work with Puff Daddy didn’t go very well. “It wasn’t even a song,” Beck told NME in 1999. “It was a failed experiment. I was singing something about how expensive my hormones were, and I just got the blankest face from him.” (In Puffy’s defence, hit hormone anthems are few and far between.)

Beck. Photograph: Peter Hapak/PR Company Handout

3 Radiohead are the most recent high-profile act to have had a proposed Bond theme rejected. (They made their song Spectre available on Christmas Day 2015, showcasing their lack of appreciation for the Bond franchise – everyone knows James Bond’s classic Boxing Day fare.)

4 Over the years artists such as Johnny Cash, Alice Cooper and Ace Of Base also had Bond songs knocked back; Pulp and Pet Shop Boys both reworked unsuccessful Bond pitches into new songs (Tomorrow Never Lies and This Must Be The Place I Waited Years To Leave respectively).

5 Still on a Pet Shop tip, when their 2010 Glastonbury headline slot rolled around, Tennant/Lowe approached Susan Boyle to take the Dusty Springfield part in What Have I Done To Deserve This?. “Her management felt she might not feel comfortable,” Tennant subsequently explained. It’s a shame, really: SuBo sprawled in the Green Fields, off her chips on poppers at five in the morning, could have been just what her career needed.

Lady Gaga and Kanye West. Composite: Getty Images

6 In 2009, Lady Gaga and Kanye West – riding high on Bad Romance and 808s & Heartbreak – announced an arena tour called Fame Kills. It would be a true joint tour – stages would be erected at opposite ends of each venue, and neither act would be the headliner or opening act. Gaga reckoned it would be “one of the most groundbreaking moments in touring history”. Dates were scheduled and teaser videos uploaded, but the tour was cancelled. Gaga’s choreographer cited creative differences but Kanye hinted that it was due to the fallout from his Taylor Swift stage invasion. The greatest crime here is that nobody got to see the merch stand.

7 Earlier this year country star Dwight Yoakam – of all people – claimed David Bowie once told him that six months prior to Elvis Presley’s death, Presley had asked Bowie to produce his next record. “It has to be one of the greatest tragedies in pop music history that it didn’t happen,” notes our reliable narrator. “One of the biggest missed opportunities.”

David Bowie and Elvis Presley. Composite: Rex/Getty

8 Separately, Bowie also claimed to have offered Golden Years to Elvis. Without wishing to extrapolate too wildly, could Bowie’s presence have steadied Elvis and saved his life? Well, it was the mid-70s, so almost certainly not.

9 Chairmen Of The Boards was a proposed 2001 album that would see Dr Dre and Timbaland collaborate, with their respective artists such as Eminem and Missy coming along for the ride. It would have been good if the “boards” theme extended to everyone performing on skateboards, but none of it was to be.

10 U2 asked Jeff Koons to work on the stage design for one of their stadium tours. Amazingly, he agreed. After several months, Koons invited the band to New York to see his backdrop idea. A curtain was triumphantly pulled back to reveal … a huge photograph of four kittens, in socks, hanging on a washing line. The collaboration didn’t go ahead. (Let’s just pause for a moment to imagine Bono’s face when the curtain went back.)

11 The modern sphere of bottom-approving doo-wop tunes could have looked rather different: Meghan Trainor originally wrote millennial rumpbanger All About That Bass for Beyoncé. When Beyoncé’s team passed, Trainor used the song to launch her own career. To be fair, it would have been the worst ever Beyoncé single.

12 One of the more unlikely shelved releases of the 80s involves ludicrous rock outfit Judas Priest and pop-dominating force Stock Aitken Waterman. “We did a little work with them for experimental reasons,” guitarist Glenn Tipton would later explain. “They are very professional and very good producers.” (One of the tracks, a cover of The Stylistics’ You Are Everything, eventually leaked many years later.)

13 Less a question of turning back time than disrupting it and creating a spooky alternative universe, Cher’s Believe had its wobbly-voice effect added only at the last minute, but the real twist is that in its earliest stages it sounded, according to writer Brian Higgins, like a Stone Roses song.

Cher. Photograph: Publicity image from music company

14 But could the Stone Roses themselves have sounded rather different? Producer John Leckie almost wasn’t on board for the band’s debut album – their first choice was acid house producer DJ Pierre, who turned the band down due to other commitments. The band are currently in the studio working on their third album and LADS, IF YOU’RE READING THIS, THERE’S STILL TIME TO GET AN OLD 303 ON EBAY.

15 Prince’s former sound engineer Susan Rogers created a vault (“an actual bank vault”) in Prince’s Paisley Park basement; when she left in 1987 it was already nearly full, hinting that princevault.com’s list of 400 unreleased Prince songs is just the tip of the iceberg.

16 That Prince site also notes that Emotional Pump, a song Prince wrote for Joni Mitchell, was rejected by the singer because “she didn’t think it matched her style”. One lyric was “you are my emotional pump, you make my body jump”.

17 “I’m not sure he liked them.” That’s how Jack White discussed the tracks he worked on for Jay Z. White was also keen to work with Kanye on Yeezus, but after responding to Kanye’s initial contact, didn’t hear back. (Skrillex is one of various other artists waiting for a followup call from Kanye.)

Jack White and Jay Z. Composite: AP

18 Chic wrote an entire album’s worth of material for Aretha Franklin. Franko rejected every song, including one perky number called Upside Down.

19 The world of largely beige mid-2000s girlband pop could have been quite different: Atomic Kitten founder Andy McCluskey’s original sonic blueprint for the band was the KLF.

20 Swedish superproducer Max Martin originally offered … Baby One More Time to TLC, who turned it down because they weren’t keen on the lyrics.

21 Noel Gallagher claims to have destroyed the master recordings of the space-rock album he recorded with Amorphous Androgynous. “He was too afraid to be weird,” the Androgynous chaps reported. “It became apparent that they weren’t making a record for me but I was making a record for them,” was Gallagher’s way of seeing it. He wasn’t having that.

22 A further Britney offcut is her 2003 work with LCD Soundsystem’s James Murphy. “It was very strange,” Murphy later recalled. “We were both lying on the floor, head-to head, working on lyrics in a notepad. She seemed eager to please, but it went nowhere. She went to dinner and just never came back.” In a parallel universe, Britney became a mid-2000s indie pop darling, never released Womanizer, and is headlining this year’s Field Day.

Britney Spears. Photograph: Paul Moseley/AP

23 In her time Britney has also rejected Rachel Stevens’ Sweet Dreams My LA Ex, which was written by Cathy Dennis as an answer record to Justin Timberlake’s Cry Me A River, as well as Rihanna’s Umbrella and Lady Gaga’s Telephone.

24 Poor old James Murphy’s work with Janet Jackson didn’t come to much, either. “Everything’s very political,” Murphy subsequently noted. Poor James Murphy. Give him a cuddle.

25 Janet had previously rejected solid gold Whitney banger How Will I Know …

26 … while Whitney was also the first choice of Janet’s brother Michael for the guest vocal on I Just Can’t Stop Loving You. Whitney – as well as Barbra Streisand – declined the invitation.

27 Prince visited Michael Jackson’s studio in 1994 with a view to recording a song together but that wasn’t the first near miss. Jackson’s Bad had originally been imagined as a duet between the pair, its non-occurrence depriving the world of seeing Prince run around an underground carpark shouting “HOOOOOOOO” a lot. Disappointing.

28 A Jacko/Madonna collaboration on In The Closet, also fell apart when Michael rejected Madonna’s provocative lyrics. Princess Stephanie of Monaco was drafted in instead, which is fairly classic Jacko.

29 It’s also worth remembering that in a parallel pop world Michael Jackson didn’t reject the songs Pharrell offered him, and which later went on to launch Justin Timberlake’s solo career. Michael would later tell Pharrell: “You should’ve gave those songs to me.” (He had a point – Michael Jackson performing Rock Your Body could have turned his career around.)

30 It’s been covered endlessly elsewhere, but it bears repeating that the opening line of the Beatles’ Yesterday was originally “Scrambled eggs / Oh my baby how I love your legs / Not as much as I love scrambled eggs”, a clearly superior lyric.

Stevie Nicks. Photograph: CHARLES KNIGHT/REX/Shutterstock

31 In 2010, Roger Ebert leaked his own screenplay for the aborted 1977 Sex Pistols film Who Killed Bambi. (It’s this script that prompted 20th Century Fox to pull funding from the film.) “I can’t discuss what I wrote, why I wrote it, or what I should or shouldn’t have written,” Ebert explained on his blog. “Frankly, I have no idea.”

32 Stevie Nicks turned down Blondie’s Call Me; she also passed on the opportunity to write lyrics for the song that became Purple Rain. “It was so overwhelming, that 10-minute track,” she later admitted. “I just got scared. I called him back and said: ‘I can’t do it. I wish I could. It’s too much for me.’”

33 Frustrated by demands to replicate her international hit I Love It, Charli XCX stropped off and made a punk album which has yet to see the light of day, which is probably for the best.

34 Foxy Brown and Lil Kim’s proposed joint album Thelma & Louise never came to be. Foxy Brown’s brother, the less exotically named Gavin, told Vibe that Def Jam’s Lyor Cohen put up $1m to make the album happen, with the likes of Jay Z ready to work on it. The studio was booked. “They never showed up,” Gav reported, “and the project never happened.”

Charli XCX. Photograph: Sara Jaye Weiss/REX Shutterstock/Sara Jaye Weiss/REX_Shutterstock

35 A full-on rock version of Bruce Springsteen’s acoustic album Nebraska, recorded (as you would expect) with the E Street Band, remains in Bruce’s sock drawer.

36 In 2008, former Take That manager Nigel Martin-Smith attempted to launch a boyband called ASBRO.

37 It was only the overrunning sessions for Wu-Tang Forever that prevented Wu-Tang Clan from working on Björk’s Homogenic.

38 Lily Allen wrote numerous songs for a stage adaptation of Bridget Jones’ Diary. In 2014, Lily leaked some of the music – one track was a love song to a fridge.

39 Kanye West, Lupe Fiasco and Pharrell Williams’s CRS project were due to record an album sampling the likes of Pink Floyd and Radiohead. West suggested the album would follow his Jay Z collaboration Watch The Throne; in 2011, Lupe Fiasco suggested the album was indefinitely shelved.

Elton John, Freddie Mercury and Rod Stewart. Composite: GETTY/REX/PENNY LANCASTER

40 Grace Jones auditioned for songwriters Gamble & Huff in the early 70s. It was a shambles, so she had to be Grace Jones instead.

41 In failed supergroup news Rod Stewart claimed in his autobiography that he once considered forming a trio with Elton John and Freddie Mercury.

42 Nas has claimed that he and Amy Winehouse planned to record a sequel to her song Me & Mr Jones. The sad thing here is what the world really needs is a sequel to Valerie. Where is Valerie in 2016? Is she happy? Has she reclaimed her PPI? Get The Zutons on the phone.

Nas. Photograph: Scott Gries/Invision/AP

43 Jimi Hendrix, meanwhile, was planning to form a band with Miles Davis and Paul McCartney. It’s fair to assume this trio would have been a bit less LOL-stuffed than Rod’s, but imagine the three-a-side football matches they could have had.

44 As one example of an unrealised idea that really could have changed music history, Tupac’s vision for the One Nation album was that it would be a collaborative effort aimed at uniting hip hop’s east and west coast stars. Then Tupac died so that was that.

45 Quintessential 80s brooder Don’t You Forget About Me was passed on by Bryan Ferry, the Pretenders and Billy Idol before Simple Minds picked it up.

Bonnie Tyler. Photograph: David Redfern/DAVID REDFERN / Redferns

46 On the topic of alternative pop decisions from another dimension, another dimension, another dimension, it’s probably best all round that the Beastie Boys’ label talked them out of calling their debut album Don’t Be A Faggot.

47 There’s confusion over whether Total Eclipse Of The Heart was originally written for Meat Loaf (Meat says that’s the case, but Bonnie Tyler’s having none of it). In any case the song was originally called Vampires in Love, and was planned for inclusion in Jim Steinman’s musical based on Nosferatu.

48 In 2014, Drake’s involvement in a proposed Aaliyah tribute album, featuring unheard vocals from the late singer, prompted such widespread horror online that producer Noah “40” Shebib shelved the entire project.

49 As we near the end of our investigation it’s worth remembering that somewhere on a far-flung hard drive there exists a pop album recorded BY LEWIS HAMILTON.

Adele. Photograph: Mike Marsland/WireImage

50 And finally, the current Adele album has left plenty of what-if moments in its wake: sessions with Phil Collins and Damon Albarn came to nothing (Phil subsequently called Adele a “slippery little fish”), while a song Adele wrote with Sia – Alive – was rejected by Adele and became the first single from Sia’s This Is Acting album, which has now given the world Cheap Thrills, thus bringing our tantalising glimpse through pop’s looking glass full circle.