He remains an enduring cultural presence even for many young people – but what would he be doing if he were alive?
The 27-year-old shot himself at his home in Seattle on April 5, 1994, ending his life, his suffering and, at least symbolically, the grunge movement. Rock has kept evolving since his suicide yet "Nevermind," Nirvana's brutal 1991 masterpiece, is still widely considered one of the most influential albums in history.
"He remains the most important musician of the last two decades in music, with an album that is still one of the last great rock records," said Charles R Cross, who has written three books on the artist including "Here We Are Now: The Lasting Impact of Kurt Cobain."
To Cross, Cobain's key contribution is opening the way for songwriters to tackle a wider emotional range. Nirvana's songs included "Lithium," a frank exploration of Cobain's manic depression, and the searing "Rape Me."
"His impact on songwriting was that he made it okay for songs to be about painful emotions, angst, depression – even something as awful as rape," Cross said.
Nirvana was at the forefront of a boom in alternative rock, as mainstream audiences increasingly listened to Seattle grunge bands who also included Pearl Jam and Soundgarden – as well as hard-edged groups from elsewhere in the United States such as Green Day and Smashing Pumpkins.
Nirvana's influence can be heard in more recent bands such as Cloud Nothings, Cage the Elephant and Fall Out Boy – but also in more unexpected areas. Rap superstar Jay Z quoted Nirvana's breakthrough hit "Smells Like Teen Spirit" in his track "Holy Grail," which featured Justin Timberlake.
Stan Cuesta, a French music journalist who has written a book on Nirvana, said the group's fan base remains surprisingly young. "Smells Like Teen Spirit" has enjoyed a recent resurgence with nearly 500 million views on YouTube.
"Nirvana's audience today isn't the people who listened to the group at the time. It's young people. It's funny as some of them weren't born when Kurt Cobain died 23 years ago," Cuesta said.
Kurt Cobain in an internet era
But Cobain – with his ragged cardigan and thick blonde locks – may be better known for some younger fans for his look rather than Nirvana's music, Cuesta said.
"Kurt's poster is in everyone's bedroom like Che Guevara's poster used to be, even if people don't necessarily know much about Che's political activities or Nirvana's music," he said.
Cobain – whose suicide note quoted Neil Young's line that "it's better to burn out than to fade away" – may have hated his contemporary image.
But what would Cobain have been like as a 50-year-old in 2017, an era when most artists feel obliged to promote themselves constantly on the internet and many make their music on laptops instead of in garages?
"I don't think Nirvana would have been around long to begin with," Cuesta said. "He said so at the time. His success was weighing heavily on him. He would have pursued a solo career different than what he was doing at the beginning."
A possible sign of what Cobain would have become could be seen in "MTV Unplugged in New York," the last recording of Nirvana which was released months after his death.
Recorded for the MTV series of the time, Cobain went mellow with an acoustic guitar. In addition to Nirvana songs, the session featured multiple covers including of David Bowie's "The Man Who Sold the World" and the folk standard "Where Did You Sleep Last Night?"
"He would have done something softer, more acoustic. He always had this blend of pop and punk," Cuesta said.
"He might have gone more experimental. One of the things that was most gratifying for him was his recording with William Burroughs," the legendary beat poet whom Cobain accompanied on guitar as he recited "The 'Priest' They Called Him."
Some of Cobain's early recordings, made on cassette as he grew up in the lumber town of Aberdeen, Washington, were released in 2015 to accompany "Montage of Heck," a documentary that had the cooperation of the rocker's widow Courtney Love.
Cuesta said it was possible to imagine a 50-year-old Cobain with a diverse solo discography that, much like Neil Young's, goes in both electric and acoustic directions.
"It's a bit of a fantasy, but I would imagine him ageing well."