Pop's comeback stars: It's good to be back...

Don't call it a comeback; I've been here for years," urged LL Cool J in the opening lines of his 1990 hit single, "Mama Said Knock You Out", from the album of the same name. In the period leading up to its release, many claimed the rapper's career was in the doldrums. His grandmother reportedly told him to "knock out" his critics, hence the title.

In fact, Mr Cool J had only been away a year: his previous album Walking with a Panther was released in 1989, and reached the top of the Billboard R&B charts. Its commercial bent may have raised eyebrows in the hip-hop community, but it was factually correct to insist that "Mama" was in no way a comeback.

Yet perhaps he ought to have encouraged the notion, for the comeback is a potent and well-used generator of hype. In 2010, for example, the public was informed of so-called comebacks by Sade (genuine – it's a decade since her last studio album); Christina Aguilera (dubious – Back to Basics was released in 2006, but she hasn't exactly retreated from the limelight in the meantime); and Eminem (preposterous – his previous album was only a year old).

In 2011, we are told to expect comebacks from, among others, Amy Winehouse (who last released new music four years ago) and possibly – if singer Agnetha Faltskog can persuade her bandmates – Abba. Sometimes a comeback is really just a continuation; sometimes it's an encore. Whether it's authentic or bogus, the people love it: nostalgia is a guilty pleasure in which we all gladly indulge.

The comeback may be most plausible as a sporting motif, its apotheosis the fights of Muhammad Ali. In politics, Bill Clinton called himself "the Comeback Kid" after his unexpectedly strong showing in the 1992 New Hampshire Democrat presidential primary. It's Hillary, however – unpopular First Lady turned highly successful Secretary of State – who has most effectively disproved F Scott Fitzgerald's maxim about second acts in American lives.

Still, it's the record industry that benefits most consistently from the comeback's marketing potential. The original musical comeback king was Elvis Presley, who'd watched his star wane during the mid-Sixties as the Beatles and their ilk monopolised the charts.

With even his movies beginning to fade in quality and popularity, the singer's manager, Colonel Parker, planned a Christmas television special, in which Elvis would croon a well-worn selection of cheesy carols. However, producer-director Steve Binder decided instead to make full use of his star's neglected and varied talents, envisioning not just a re-run but a re-birth. The subsequent show mixed intimate live performance with some extravagantly choreographed recordings. An extraordinary success, it became known as the '68 Comeback Special.

Frank Sinatra famously copied the trick: after announcing his retirement from showbusiness in 1971, he recorded a bestselling comeback album and TV special, Ol' Blue Eyes is Back, just two years later. Lily Allen, take note.

Surely 2010's most high-profile and successful comeback was Take That's. Reunited for the first time as a five-piece, the group starred in their own television special, Look Back, Don't Stare, which was shot in moody black and white to demonstrate both their maturity and the depths of melancholy from which all five bandmates had risen to re-conquer the pop world.

Not only did their LP and tickets for the imminent tour sell at record speed, but Take That's reinvention as a "manband" also allowed them a whole new audience of grown men struggling neurotically, like Howard, Jason et al, to come to terms with encroaching middle age.

Pulse films, the company behind Look Back, Don't Stare, was responsible, too, for No Distance Left to Run, a moving documentary record of Blur's 2009 comeback shows at Glastonbury and Hyde Park. So successful were those concerts – and so clear the enjoyment the band derived from them – that Blur are now planning a return to the studio, 12 years since the original line-up last recorded an album together.

Blur's success inevitably presaged a wave of Nineties Britpop nostalgia, and both Suede and Pulp have reformed to take advantage. Kula Shaker were on the road again before Blur, with Cast not far behind them. Even Toploader have announced plans for a reunion album and tour in 2011. Don't snigger too loudly: a well-timed comeback can generate a kind of amnesiac goodwill for previously reviled public figures. If it worked for the twice-sacked Peter Mandelson, it can work for Toploader.

For an artist, the motivation for a comeback can be myriad: financial hardship, potentially ameliorated by a sell-out reunion tour and a spike in iTunes downloads; irresistible pressure from a still-enthusiastic fanbase; even a band's own genuine pining for the glory days of old.

In the most celebrated cases, it's even possible that they've found something new to say. Johnny Cash earned renewed critical and popular acclaim in his final years for the magnificent American albums, recorded with producer Rick Rubin, on which he grappled with the looming prospect of his own death. Like Rubin – who has also produced two Neil Diamond albums – Quentin Tarantino uses the rose-tinted specs of nostalgia to coax cinematic comebacks out of neglected talents: John Travolta in Pulp Fiction, David Carradine in Kill Bill, Pam Grier in Jackie Brown.

A comeback can be executed with varying degrees of dignity. When they reformed in 1996, the Sex Pistols faced head-on any accusations that they were selling out their punk legacy, naming their series of unfortunate reunion shows "The Filthy Lucre Tour". The return of the Spice Girls in 2007 was accompanied by a Tesco advertisement for which Posh and co were reportedly paid £1m each.

Led Zeppelin, on the other hand, retained their considerable integrity by playing a single benefit concert at the 02 in 2007, which was praised to the heavens by adoring reviewers. Though Jimmy Page briefly made encouraging noises about a subsequent world tour and album, Robert Plant was busy enjoying his acclaimed collaboration with country singer Alison Krauss. In 2010 Plant recorded another great solo album: the sound of a man refusing to live in the past.

Something about seeing four old fellows onstage for Led Zeppelin's brief reunion did, however, raise the spectre of the comeback's less dignified cousin: the endless retirement tour. Cher, co-star of Christina Aguilera's supposed comeback film, Burlesque, circled the globe for her three-year "Farewell Tour" between 2002 and 2005 – only to begin performing again in 2009. Barbra Streisand retired from live performance in 2000, then returned for another string of retirement shows in 2006. The Rolling Stones have been on a perpetual retirement tour for the past 25 years.

A band, of course, can break up and then sensationally reform, like Madness or The Pixies. A solo artist has a harder job convincing anyone that a "comeback" isn't simply their new album, completed on an entirely unremarkable timescale. Cat Stevens – now Yusuf Islam – converted to Islam, then left a 28-year gap between LPs. That works, but not everyone can follow the same route.

For many artists, the surest way to engineer a convincing comeback is to follow the celebrity path of a public fall from grace, followed at length by personal and artistic redemption. Robbie Williams won wild success as a solo artist, followed by a slow mental and creative decline, only to be rescued from self-destruction by a return to the Take That fold – a perfect narrative arc.

Eminem pointedly named his last two albums Relapse and Recovery, a knowing reference to his one-time prescription-drug addiction. The Libertines' return in 2010 was coloured by Pete Doherty's public drug use, disastrous love life and apparent rehabilitation. Amy Winehouse will no doubt play a similar tune upon her return in 2011. It's a cycle that can become perpetual, however: for professional reality stars such as Jordan or Kerry Katona, personal crises and against-the-odds emotional comebacks are a frequent necessity; they always need a new reason to be photographed by OK! magazine.

On the other hand, as Johnny Cash could attest, tough experience can lend credibility to a comeback. Mickey Rourke crowned his return to the screen with an Oscar-nominated performance as The Wrestler. To many, the troubled fighter he portrayed was simply a version of his own biography.

The appearance of Rourke and Robert Downey Jr – both former bad boys and comeback kids – added edge to a glossy Hollywood blockbuster, Iron Man 2. It also prompted an obvious question: how the heck did anyone persuade Marvel Studios to pay that insurance bill?

Comebacks are generally discussed because of their success, but there have been plenty of less auspicious attempts to reclaim the limelight. Until the band's overdue break-up last year, every new Oasis record was heralded as a return to form, despite Noel Gallagher's constant refrain that his best work was behind him. Rather than split and reform like Blur or Suede, their fellow Nineties acts the Stone Roses and Elastica each took five years to record disappointing follow-ups to their brilliant debuts – and then split.

And what about the Beatles? In 1995, the Fab Four produced two previously unheard singles and, yes, a television special. Except that there were only three of them – "The Threetles!" – adding their input to a pair of unremarkable Lennon demos: "Free as a Bird" and "Free Love". The fifth Beatle, astute producer George Martin, kept well clear.

When Take That first reformed without Williams, their erstwhile rivals East 17 decided to do the same. But after a one-off gig in 2006, old tensions bubbled up again: Brian Harvey and Tony Mortimer brawled, while John Hendy (one of the less well-known band members) faced scheduling conflicts with his roofing business. An unintentionally comic Channel 4 documentary, East 17: The Reunion, did them no favours. Take That's Progress has now sold well over two million copies worldwide. East 17's hoped-for resurgence is still pending.