Meanwhile, head to NME.COM/video to hear NME writers discuss these artists - and don't forget to let us know your own personal cult heroes.
From being asked by Kurt Cobain to support Nirvana, to The Futureheads' cover of 'A Picture Of Dorian Gray', to being the glue that bound the C86/Creation scene of the late '80s, Television Personalities have nonetheless never troubled the mainstream.
Here’s Andrew from MGMT on their genius: “We set up a couple of shows with them – they were wild shows. When TVP play they can be completely disastrous, or just really good. It confused the hell out of our fans. They've made some of the best music of the last 30 years.”
Download: ‘Part Time Punks’
Like so many in the hip-hop scene, it took death for the work of James Dewitt Yancey, to be given the appropriate reverence.
Not by Jack Barnett from These New Puritans though: "My brother lent me a copy of 'Donuts' – two days before he died, weirdly.
"He was unique for his approach to rhythms, a kind of out-of-timeness. I admire his imperfections; he was definitely the most standout figure from that entire independent hip-hop scene."
Download: Anything on 'Donuts'
With Atari Teenage Riot, Alec Empire invented digital hardcore and reconnected techno with politics, while as the label boss of Digital Hardcore Recordings, he's been the leading light in the Berlin electronic avant-vanguard.
In his present infinity of solo guises, and with a May ATR reunion and new single confirmed, he still has no idea how to behave.
Download: Atari Teenage Riots – 'Destroy 2000 Years of Culture'
While others schemed it, he lived it.
While most moaned about the state of the charts and banality of record labels, he put the entire music industry over his lap and gave it a spanking – whether it was The KLF deleting their entire back-catalogue, costing themselves a fortune, or them toasting another fortune in the infamous burning-a-million-quid saga.
Drummond has always gone out and brought us back the news about the relationship between art, music, and commerce.
Download: The KLF – 'What Time Is Love?'
Despite being the first DIY-punk-pop-riot-grrrl-band-who-wrote-their-own-fanzines to appear on Top Of The Pops, this Glasgow trio were the subject of much derision.
Yet in recent years their cult has striven to right past wrongs; last month even saw their fans hold International Bis Day, with tribute bands playing in venues worldwide.
We asked singer Manda Rin whether it upset her that most people hated the band: "Not really – There's nothing worse than being mediocre or not remembered. I'd rather be the Marmite than Asda bread. People still get in touch to tell me how much we meant to them."
Download: 'Secret Vampires'
Born Steven John Hamper in 1959, Childish is an English artist, painter, author, poet, photographer, filmmaker, singer and guitarist.
He is loved by Graham Coxon: "I watched Thee Headcoats play at St John's Tavern [in Archway, London] in the mid-'90s. That was long before I met Billy – I think Thee Headcoats were coming to an end by the time I actually went to go talk to him.
"I said, 'Can I release a single on my label please?' and he went, 'Yeah, alright.' And that was it! I think Billy’s very popular among a lot of famous guitar players, from Eddie Vedder to Beck to Jack White. He's a bit of a musician's musician. It's because he likes to protect what needs to be protected – he's a cult musician because he's uncomfortable with the mainstream and sees it as fraudulent."
Download: Thee Headcoats – 'We Hate The Fuckin' NME'
In hip-hop, so often you don't know what you got 'til it's gone. Never more true than with Lamont Coleman, dead by bullet at 24, possibly in a tragic case of mistaken identity.
When you hear L in full flow it's easy to see why he's often cited by the more gangsta-rap fraternity as the most gifted MC ever. L had an utterly baffling sense of rhyme acrobatics, together with a mastery of metaphor and simile, but also a fire, speed, and intensity that was just the right balance of spectral street prophet and stone-cold psychopath.
Lydia Lunch is a spoken-word performance artist who has, at times, made GG Allin look like the kind of chap you'd take home for tea with your grandparents.
In New York in 1976, aged 17, she formed Teenage Jesus And The Jerks, an abrasive no-wave noise band who took punk's rudimentary three chords and ripped them apart with knives and beer bottles.
To this day she's a prolific performer and writer and gives possibly the best interviews of all time. Here's her take on Madonna, from 2008: "I think people like Madonna do everyone a fucking disservice, running round in a leotard at her fucking age, talking about nothing but fucking dancing."
Download: Teenage Jesus And The Jerks – 'Orphans'
For over 20 years the 42-year-old Californian has been confounding audiences, fronting a succession of bands who push the envelope with every note.
Simon Neil from Biffy Clyro is an acolyte: "We love him because he’s always shown the right amount of contempt for the industry and has always followed his own muse. It's a lesson that more bands could follow…"
Download: Mr Bungle – 'My Ass Is On Fire'
When we were putting together this issue, everyone in the NME office argued about who should be in this list. Nearly everyone said Sparklehorse. Then when Mark Linkous passed away the doubters joined them in agreement.
Radiohead’s Colin Greenwood was certainly never a doubter: “I was very sad to hear the news that Mark Linkous had died. He and his band toured with Radiohead in Europe. His first two records were important to me, and I carried his music from the tour into my life, and my friends’ lives too. He was softly spoken, with an Old South courtesy I hadn’t heard before: he introduced me to Daniel Johnston’s music, and the writing of Pinckney Benedict. Mark made beautiful music, and we’re lucky to have it. Rest in peace.”
Download: Sparklehorse – ‘Sad & Beautiful World’