His daughter Mercedes told the Associated Press he died of pneumonia on Tuesday night in Los Angeles surrounded by family and friends.
California-born Kilmer was diagnosed with throat cancer in 2014 but later recovered, she said.
The actor, who played Tom 'Iceman' Kazansky in Top Gun alongside Tom Cruise in 1986, previously admitted he didn't want the role which made him famous.
But he said he begged to be part of the sequel, Top Gun: Maverick in 2022, even going as far as contacting the producers and creating "heartrending scenes with Iceman". It would be his final acting role.
Kilmer had a colourful romantic past, having dated Hollywood stars including Cindy Crawford, Angelina Jolie, Carly Simon and Cher.
He starred in Willow in 1988 and married his British co-star Joanne Whalley. The couple had two children before they divorced in 1996.
Kilmer portrayed Batman in the 1995 film Batman Forever and received critical acclaim for his portrayal of rock singer Jim Morrison in the 1991 movie The Doors.
He also starred in True Romance and Kiss Kiss Bang Bang, as well as playing criminal Chris Shiherlis in Michael Mann's 1995 movie Heat and Doc Holliday in the 1993 film Tombstone.
Kilmer was one of the best-paid actors in the 1990s, and in 1992 film critic Roger Ebert wrote: "If there is an award for the most unsung leading man of his generation, Kilmer should get it."
The actor made his film debut in the spy spoof Top Secret! in 1984 before appearing in the goofy comedy Real Genius in 1985 - a year before he rocketed to fame in Top Gun.
'I make no apologies'
Over the years, Kilmer had numerous spats with directors and co-stars and gained a reputation for being temperamental, intense, a perfectionistic, and sometimes egotistical.
In an interview in 2003, Kilmer said: "When certain people criticise me for being demanding, I think that's a cover for something they didn't do well. I think they're trying to protect themselves.
"I believe I'm challenging, not demanding, and I make no apologies for that."
Kilmer famously clashed with co-star Marlon Brando during the notoriously troubled production of "The Island of Dr. Moreau", which flopped in 1996.
John Frankenheimer, who directed the movie, said afterwards that there were two things he would never do: "I will never climb Mount Everest and I will never work with Val Kilmer again. There isn't enough money in the world."
Meanwhile, Batman Forever director Joel Schumacher once described Kilmer as "the most psychologically troubled human being I've ever worked with".
The Chicago Tribune wrote in 1997 that Kilmer was "a member in good standing of Hollywood's bad boys club".
Despite his many plaudits for his roles in critically-acclaimed movies, Kilmer was also nominated multiple times for worst actor in the annual Razzie awards, honouring the worst in cinema.
'You truly were an icon'
In his 2020 memoir Your Huckleberry, Kilmer discussed his throat cancer diagnosis and recovery.
He underwent radiation and chemotherapy treatments for the disease and also had a tracheostomy that permanently gave him a raspy speaking voice.
As well as the sequel to Top Gun, following his cancer diagnosis, Kilmer also starred in films including The Snowman in 2017 and Paydirt in 2020.
Actor Josh Brolin wrote on Instagram: "See ya, pal. I'm going to miss you. You were a smart, challenging, brave, uber-creative firecracker. There's not a lot left of those.
"I hope to see you up there in the heavens when I eventually get there. Until then, amazing memories, lovely thoughts."
In an Instagram post, actor Josh Gad called Kilmer "an icon".
He said: "RIP Val Kilmer. Thank you for defining so many of the movies of my childhood. You truly were an icon."
Kilmer made his Broadway debut in the 1983 production of Slab Boys with Sean Penn and Kevin Bacon.
He also appeared in Shakespeare plays in New York - playing the title role in Hamlet and appearing in Henry IV: Part One and As You Like It.
In 2005, he starred on London's West End in Andrew Rattenbury's adaptation of The Postman Always Rings Twice at the Playhouse Theatre.
Kilmer also enjoyed painting, with his website describing him as a "talented and prolific artist in a variety of mediums".
Born in Los Angeles on 31 December 1959, Kilmer began acting in high school and became the youngest student accepted into the drama division of the famed Juilliard School in New York.
Phillip Noyce, who directed him in "The Saint," told the Chicago Sun-Times in 1997 that Kilmer "is plagued by a bad image, but most of it is unjustified. The real Val Kilmer is a lamb. And he is the hardest-working actor I've ever seen".