Williams was born at St. Luke's Hospital in Chicago, Illinois on July 21, 1951. His father, Robert Fitzgerald Williams, was a senior executive in Ford Motor Company's Lincoln-Mercury Division. His mother, Laurie McLaurin, was a former model from Jackson, Mississippi. Her paternal great-grandfather was Mississippi senator and governor Anselm J. McLaurin. Williams had two elder half-brothers named Robert and McLaurin. He had English, Irish, Scottish, Welsh, German, and French ancestry.

In late 1963, when Williams was 12, his father was transferred to Detroit. The family lived in a 40-room farmhouse on 20 acres in suburban Bloomfield Hills, Michigan, where he was a student at the private Detroit Country Day School. He excelled in school, where he was on the school's soccer team and wrestling team, and was elected as class President.

As his father traveled frequently for work and his mother also worked, Williams was attended to by the family's maid, who was his main companion. When Williams was 16, his father took early retirement and the family moved to Tiburon, California. Following their move, Williams attended Redwood High School in nearby Larkspur. At the time of his graduation in 1969, he was voted "Most Likely Not to Succeed" and "Funniest" by his classmates.

During the late 1970s and early 1980s, Williams had an addiction to cocaine. He was a Casual friend of John Belushi, and the sudden death of Belushi in 1982 due to a drug overdose which happened the morning after the two had partied together, along with the birth of his own son Zak, prompted him to quit drugs and alcohol: "Was it a wake-up call? Oh yeah, on a huge level. The grand jury helped, too." Williams later referring to this event said, "It sobered the shit out of me." Williams turned to exercise and cycling to help alleviate his depression shortly after Belushi's death; according to bicycle shop owner Tony Tom, Williams said, "cycling saved my life."

In 1973, Williams attained a full scholarship to the Juilliard School (Group 6, 1973–1976) in New York City. He was one of 20 students accepted into the freshman class and one of two students to be accepted by John Houseman into the Advanced Program at the school that year; the other was Christopher Reeve. william Hurt and Mandy Patinkin were also classmates. According to biographer Jean Dorsinville, Franklyn Seales and Williams were roommates at Juilliard. Reeve remembered his first impression of Williams when they were new students at Juilliard:

Williams left Juilliard during his junior year in 1976 at the suggestion of Houseman, who said there was nothing more Juilliard could teach him. Gerald Freedman, another of his teachers at Juilliard, notes that Williams was a "genius" and that the school's conservative and classical style of training did not suit him. No one was surprised that he left.

The first film role credited to Robin Williams is a small part in the 1977 low-budget comedy Can I Do It... 'Til I Need Glasses?. His first major performance is as the title character in Popeye (1980). There, Williams showcased the acting skills previously demonstrated in his television work; and the film's commercial disappointment was not blamed upon his role. He stars as the leading character in The World According to Garp (1982), which Williams considered "may have lacked a certain madness onscreen, but it had a great core". He continued with other smaller roles in less successful films, such as The Survivors (1983) and Club Paradise (1986), though he said these roles did not help advance his film career.

Williams married his first wife Valerie Velardi in June 1978, following a live-in relationship with Comedian Elayne Boosler. Velardi and Williams met in 1976 while he was working as a bartender at a tavern in San Francisco. Their son Zachary Pym "Zak" Williams was born in 1983. Williams and Velardi divorced in 1988.

Mork became an extremely popular character, featured on posters, coloring books, lunch-boxes, and other merchandise. Mork & Mindy was such a success in its first season that Williams appeared on the March 12, 1979, cover of Time magazine. The cover photo, taken by Michael Dressler in 1979, is said to have "[captured] his different sides: the funnyman mugging for the camera, and a sweet, more thoughtful pose that appears on a small TV he holds in his hands" according to Mary Forgione of the Los Angeles Times. This photo was installed in the National Portrait Gallery in the Smithsonian Institution shortly after the actor's death to allow visitors to pay their respects. Williams was also on the cover of the August 23, 1979, issue of Rolling Stone magazine, with the cover photograph taken by famed Photographer Richard Avedon.

After his first starring film role in Popeye (1980), Williams starred or co-starred in various films that achieved both critical acclaim and financial success, including Good Morning, Vietnam (1987), Dead Poets Society (1989), Aladdin (1992), The Birdcage (1996), and Good Will Hunting (1997). He also starred in widely acclaimed films such as The World According to Garp (1982), Moscow on the Hudson (1984), Awakenings (1990), The Fisher King (1991), One Hour Photo (2002), and World's Greatest Dad (2009), as well as box office hits such as Hook (1991), Mrs. Doubtfire (1993), Jumanji (1995), and Night at the Museum (2006).

Other roles Williams had in acclaimed dramatic films include Moscow on the Hudson (1984), Awakenings (1990), What Dreams May Come (1998), and Bicentennial Man (1999). In Insomnia, Williams portrayed a Writer / killer on the run from a sleep-deprived Los Angeles policeman (played by Al Pacino) in rural Alaska. Also in 2002, in the psychological thriller One Hour Photo, Williams played an emotionally disturbed photo development technician who becomes obsessed with a family for whom he has developed pictures for a long time. The last Williams movie released during his lifetime was The Angriest Man in Brooklyn, a film addressing the value of life. In it, Williams played Henry Altmann, a terminally ill man who reassesses his life and works to redeem himself.

In 1986, Williams teamed up with Whoopi Goldberg and Billy Crystal to found Comic Relief USA. This annual HBO television benefit devoted to the homeless has raised $80 million as of 2014. Bob Zmuda, creator of Comic Relief, explains that Williams felt blessed because he came from a wealthy home, but wanted to do something to help those less fortunate. Williams made benefit appearances to support literacy and women's rights, along with appearing at benefits for veterans. He was a regular on the USO circuit, where he traveled to 13 countries and performed to approximately 100,000 troops. After his death, the USO thanked him "for all he did for the men and women of our armed forces."

His first major break came from his starring role in Director Barry Levinson's Good Morning, Vietnam (1987), which earned Williams a nomination for the Academy Award for Best Actor. The film is set in 1965 during the Vietnam War, with Williams playing the role of Adrian Cronauer, a radio shock jock who keeps the troops entertained with comedy and sarcasm. Williams was allowed to play the role without a script, improvising most of his lines. Over the microphone, he created voice impressions of people, including Walter Cronkite, Gomer Pyle, Elvis Presley, Mr. Ed, and Richard Nixon. "We just let the cameras roll," said Producer Mark Johnson, and Williams "managed to create something new for every single take."

Terry Gilliam, who co-founded Monty Python and directed Williams in two of his films, The Fisher King and The Adventures of Baron Munchausen (1988), noted in 1992 that Williams had the ability to "go from manic to mad to tender and vulnerable," adding that to him Williams was "the most unique mind on the planet. There's nobody like him out there."

On April 30, 1989, he married Marsha Garces, Zachary's nanny, who was pregnant with his child. They had two children, Zelda Rae Williams (born 1989) and Cody Alan Williams (born 1991). In March 2008, Garces filed for divorce from Williams, citing irreconcilable differences. Their divorce was finalized in 2010. Williams married his third wife, graphic designer Susan Schneider, on October 22, 2011, in St. Helena, California. The two lived at their house in Sea Cliff, San Francisco, California.

Williams continued to provide voices in other animated films, including FernGully: The Last Rainforest (1992), Robots (2005), Happy Feet (2006), and an uncredited vocal performance in Everyone's Hero (2006). He also voiced the holographic Dr. Know character in the live-action film A.I. Artificial Intelligence (2001). He was the voice of The Timekeeper, a former attraction at the Walt Disney World Resort about a time-traveling robot who encounters Jules Verne and brings him to the Future.

His penetrative acting in the role of a therapist in Good Will Hunting (1997) deeply influenced some real therapists and won Williams an Academy Award. In Awakenings (1990), Williams played a Doctor modeled on Oliver Sacks, who wrote the book on which the film was based. Sacks later said the way the actor's mind worked was a "form of genius." In 1989 Williams played a private school Teacher in Dead Poets Society, which included a final, emotional scene which some critics said "inspired a generation" and became a part of pop culture. Looking over most of his filmography, one Writer was "struck by the breadth" and radical diversity of most roles Williams portrayed.

Williams and his second wife Marsha founded a philanthropic organization called the Windfall Foundation to raise money for many charities. In December 1999, he sang in French on the BBC-inspired music video of international celebrities doing a cover of The Rolling Stones single "It's Only Rock 'n Roll (But I Like It)" for the charity Children's Promise.

While his mother was a practitioner of Christian Science, Williams was raised in the Episcopal Church, to which his father belonged. Williams wrote a list: "Top Ten Reasons to be an Episcopalian." During a television interview on Inside the Actors Studio in 2001, Williams credited his mother as being an important early influence for his sense of humor. He also said that he tried to make her laugh to gain attention.

His stand-up work was a consistent thread through his career, as seen by the success of his one-man show (and subsequent DVD) Robin Williams: Live on Broadway (2002). He was voted 13th on Comedy Central's list "100 Greatest Stand-ups of All Time" in 2004.

In 2003, Williams started drinking alcohol again while working on a film in Alaska. In 2006, he checked himself in to a substance-abuse rehabilitation center in Newberg, Oregon, saying he was an alcoholic.

Williams and Reeve remained close friends until Reeve's death in 2004. Reeve had struggled for years with being quadriplegic after a horse-riding accident. Son Zak Williams remembered their friendship as having been like "brothers from another mother". Williams paid many of Reeve's medical bills and gave financial support to his family.

In 2006, he starred in The Night Listener, a thriller about a radio show host who realizes that a child with whom he has developed a friendship may or may not exist; that year, he starred in five movies, including Man of the Year, was the Surprise Guest at the Nickelodeon Kids' Choice Awards and appeared on an episode of Extreme Makeover: Home Edition that aired on January 30, 2006.

In March 2009, he was hospitalized due to heart problems. He postponed his one-man tour for surgery to replace his aortic valve. The surgery was completed on March 13, 2009, at the Cleveland Clinic.

Years afterward, Williams acknowledged his failure to maintain sobriety, but said he never returned to using cocaine, declaring in a 2010 interview:

Williams appeared opposite Steve Martin at Lincoln Center in an off-Broadway production of Waiting for Godot in 1988. He made his Broadway acting debut in Rajiv Joseph's Bengal Tiger at the Baghdad Zoo, which opened at the Richard Rodgers Theatre on March 31, 2011. He headlined his own one-man show, Robin Williams: Live on Broadway, that played at the Broadway theatre in July 2002.

Williams's death instantly became global news. The entertainment world, friends, and fans responded to his death through social and other media outlets. His wife, Susan Schneider, said: "I lost my husband and my best friend, while the world lost one of its most beloved artists and beautiful human beings. I am utterly heartbroken." His daughter Zelda Williams responded to his death by stating that the "world is forever a little darker, less colorful and less full of laughter in his absence". U.S. President Barack Obama said of Williams: "He was one of a kind. He arrived in our lives as an alien – but he ended up touching every element of the human spirit."

On social media in August 2014, several fans paid tribute to Williams with photo and video reenactments of the 1989 film Dead Poets Society's "O Captain! My Captain!" scene.

Williams became a devoted cycling enthusiast, having taken up the sport partly as a substitute for drugs. Eventually, he accumulated a large bicycle collection of his own and became a fan of professional road cycling, often traveling to racing events, such as the Tour de France. In 2016, his children donated 87 of his bicycles in support of the Challenged Athletes Foundation and Christopher & Dana Reeve Foundation.