Jones was born in West Lafayette, Indiana and attended Paseo del Rey Elementary School, and, later, Orville Wright Junior High School. Her maternal grandparents were Lebanese, and Jones' middle name means "Little Friend" in Arabic.
At the time of her birth, Jones' father John Paul Jones was an engineering graduate and faculty board member at Purdue University, where her mother Mary Paula Jones (née Tweel) was a zoology student. Soon after the birth of Anissa's brother John Paul Jones, Jr., the family moved to Playa Del Rey, California, where John Paul, Sr. took a job in aerospace engineering.
When Jones was two years old, her mother enrolled her in dance classes. In 1964, when Jones was six, Mary Paula took her daughter to an open audition for a breakfast cereal commercial, which became Jones' first television appearance.
Jones was eight when her acting skills drew the attention of television producers, and she was cast as Ava Elizabeth "Buffy" Patterson-Davis on the CBS sitcom Family Affair (1966). In the opening plotline, Buffy, her twin brother Jody (Johnny Whitaker), and older sister Cissy (Kathy Garver) are sent to live with their Uncle Bill (Brian Keith) and his valet Mr. French (Sebastian Cabot) a year after the children's parents die in a car accident (The DVD collection notes mistakenly state "plane accident"). By July 1969, the series had become a hit, and Jones became a popular child celebrity. She also played the role of Carol Bix in the Elvis Presley comedy film The Trouble with Girls (1969).
Family Affairwas a grueling, full-time, year-round job for Jones: she was often either shooting the show or promoting it in public, seven days a week. Through each of the first three seasons, up to 30 programs were filmed for broadcast. This contrasts with later American episodic television that produce runs of 24 shows per season or less, allowing more breaks in filming and requiring fewer promotional appearances for the principal actors. In April 1969, Jones broke her right leg in a playground accident, and the producers had her injury written into the show's scripts.
Jones' Buffy character had a doll named Mrs. Beasley, which she claimed talked to her, often making funny comments. When the show became a hit, the doll was marketed by Mattel and became a best-seller in North America. Mattel also marketed two other dolls, patterned after Buffy: one in the size of its "Tutti" line of dolls and another in its talking "Small Talk" line, which featured eight different phrases (using Jones' voice). Jones took part in several other lucrative Family Affair product marketing campaigns such as Buffy paper dolls, lunch boxes, a clothing line, coloring books, and a 1971 cookbook with her picture on the cover.
Jones appeared on The Dick Cavett Show on February 25, 1971, along with actor/singer Sammy Davis Jr., and pianist Garrick Ohlsson; it was her final guest appearance on television.
Family Affair was cancelled abruptly by CBS's "rural purge" campaign in 1971, after five seasons and 138 episodes. By then, Jones was 13 years old and said she was happy at the thought of no longer needing to be seen with the Mrs. Beasley doll. She wanted to act in films, but Jones could not find the kind of work she wanted. She auditioned for the part of Regan MacNeil in the film The Exorcist (released in 1973), but the director, William Friedkin, felt that, with Family Affair still in popular consciousness at the time through syndicated daytime reruns, movie audiences might have thought Buffy was the one being possessed. Linda Blair was cast instead.
Meanwhile, Brian Keith kept in touch with Jones through letters and offered her a young-adult role on The Brian Keith Show (1972–1974). Keith told her she would not need to audition for the part, but, by then, Jones no longer wanted to work in television.
Jones believed she had been typecast. She enrolled in Los Angeles' Westchester High School and returned to a life outside the entertainment industry.
Jones' parents had initiated a bitter divorce in 1965 and carried on a long feud over custody of Anissa and her younger brother, Paul. In 1973, custody of both children was awarded to their father, but he died of heart disease shortly thereafter.
While her brother went to live with their mother, Jones moved in with a friend and began skipping school. Her mother reported Jones to the police as a runaway. Jones was arrested and sent to juvenile hall, and spent many months in state custody, after which she was allowed to live with her mother.
However, Jones soon began shoplifting and taking drugs. In 1975, she dropped out of high school altogether and briefly worked at Winchell's Donuts shop in Playa Del Rey. She reportedly felt embarrassed whenever customers recognized who she was.
On her 18th birthday, in March 1976, Jones gained control of her saved earnings from her work in Family Affair, about $180,000 (equal to $757,579 today) as well as an undetermined amount of U.S. Savings Bonds, both of which had been held for her in a trust fund. Jones and her brother Paul then rented an apartment together, not far from their mother.
Shortly before noon on August 28, 1976, after partying all night in the beach town of Oceanside, California, with her new boyfriend Allan "Butch" Koven and others, Jones was found dead in a bedroom of a house belonging to the father of a 14-year-old friend named Helen Hennessy. The coroner's report listed her death as a drug overdose, later ruled accidental; cocaine, PCP, Quaalude, and Seconal were found in her body during an autopsy toxicology examination. The police report also indicated a small vial of blue liquid next to Jones at the scene, which was never identified. The coroner who examined Jones reported she died from one of the most severe drug overdoses he had ever seen. Jones was 18 years old.
Jones had no funeral. She was cremated, and her ashes were scattered over the Pacific Ocean. She left $63,000 in cash and more than $100,000 in savings bonds when she died.
Six days after Jones' death, Dr. Don Carlos Moshos was arrested and charged with illegally prescribing Seconal to Jones, among other drugs-for-profit charges from a concurrent undercover criminal investigation. An envelope with Moshos' business address was present at Jones' scene of death, specifying a drug found in Anissa's toxicology report (Seconal), its dosage (1.5 gr), quantity (50), and the recipient's last name (Jones). Moshos was charged with 11 offenses, including second-degree murder; while awaiting trial, Moshos died of cancer by acute viral hepatitis on December 27, 1976, four months after Jones. Although the murder charges were dropped before his death, Moshos' estate was sued by Jones' surviving family for $400,000; in July 1979, the verdict found him 30% liable and Jones 70% responsible for her death, and the resulting judgment was reduced to $79,500.
On March 15, 1984, Jones' brother Paul also died of a drug overdose. He was 24 years old. On January 14, 2012, their mother, Mary Paula Tweel, died in Detroit, Michigan. Jones' father, John Paul Jones, Sr., had died of heart failure on March 7, 1974, and there were no surviving heirs to the family name.
In 1978, Canadian punk-rock group The Diodes recorded Child Star, detailing Anissa's death by overdose in a sound and style reminiscent of The Ramones. In 1983, Hillary Carlip and her band, Angel and the Reruns, recorded "Buffy Come Back", a satiric tribute to the late Jones, set to the refrain of the Family Affair theme song.