Cliburn was given a ticker-tape parade in New York upon his return from the competition and appeared on television shows such as Person to Person, What's My Line? and The Tonight Show. His recording of Tchaikovsky's First Piano Concerto shared the top of the LP charts with Johnny Mathis's Greatest Hits album and the soundtrack from South Pacific. It became the first classical music album to sell a million copies within two years.

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Cliburn was much in demand on the concert tour. He gave almost one hundred performances a year. His appearances in 1960 included a tour of the Soviet Union, where he was an audience favorite.

By the mid-1960s, however, the adulatory reviews for Cliburn were becoming mixed. Critics complained that he had not expanded his repertoire much beyond the works that had brought him the Tchaikovsky prize and showed little interest in doing so. Although Cliburn's repertoire was in fact wider than such comments suggested, it is true that the core of his program changed little over time.

By the beginning of the 1970s Cliburn's grueling concert schedule had taken a toll on him. His playing had become erratic, and critics continued to harp on his lack of musical growth. In 1974 Cliburn announced that after completing the concerts to which he was then committed, he would take a respite from the stage. After September 1978 he did not perform publicly until 1989, when he began accepting a limited number of concert dates.

Cliburn retired to a lavish house in Fort Worth, Texas, and became prominent on the local music scene. Among the projects to which he devoted his time was the Van Cliburn International Piano Competition, which he founded in 1962 and which is held quadrennially in Fort Worth.

In 1996 Thomas Zaremba filed a palimony suit against Cliburn, claiming that because of "an oral and/or implied partnership agreement," he was entitled to a share of Cliburn's income and property. Zaremba said that he had assisted in the management of Cliburn's career and finances as well as performing domestic services such as helping Cliburn care for his aged mother.

Zaremba further alleged that Cliburn may have exposed him to AIDS during their seventeen-year relationship, which lasted until around the end of 1994, after which Zaremba moved to Center Line, Michigan, where he found work as a mortician.

Cliburn called the accusations "salacious" but otherwise had little to say about the case. Indeed, though always described as gracious and polite, Cliburn was known to be notoriously difficult to interview. Music insiders had long been aware of his homosexuality, and he and Zaremba had appeared together at public functions in Fort Worth, but in Cliburn's thirty-plus years as a celebrity, the press had never linked him romantically with anyone.

The public's image of him was still that of the All-American Boy--he seemed almost frozen in time at the moment of his victory in Moscow. He lived with his mother until her death at 97, was a lifelong Baptist and a regular church-goer, did not drink or smoke, and began his concerts with The Star-Spangled Banner.

Zaremba's lawsuit was eventually dismissed because of the lack of a written agreement, which is required under Texas law.

In December 2001 Cliburn was among the artists feted at the Kennedy Center Honors. National security adviser Condoleezza Rice, herself a pianist, praised Cliburn's "grace and lyricism" and "the power of his music to build bridges across the cultural and political divide."

Cliburn was a long-time member of Fort Worth's Broadway Baptist Church to which he donated one of the largest organs in the United States, the Rildia Bee O'Bryan Cliburn Organ, named in honor of the pianist's beloved mother.

In 2008, the Broadway Baptist Church was roiled by controversy when it decided to include photos of gay and lesbian couples in its church directory. During the controversy, which was finally settled when the church was expelled from the Southern Baptist Convention for welcoming gay and lesbian couples into full membership, Cliburn was frequently mentioned as a gay member of the congregation.