Swooping, trembling and ululating, Whitney Houston opened the 36th annual Grammy Awards ceremonies last night with the song that garnered the top awards: "I Will Always Love You." The awards, given in 79 musical categories, were announced in a ceremony at Radio City Music Hall broadcast on CBS.

"I Will Always Love You" was part of the soundtrack of "The Bodyguard," which sold more than 10 million copies in the United States, making it the most popular album of 1993. It won the Grammy for album of the year. The song was named record of the year, given to a single. It also won the award for pop vocal, female, a choice that was such a foregone conclusion that the award was announced by the song's writer, Dolly Parton, and its producer, David Foster. Mr. Foster was also named producer of the year (nonclassical). Because "I Will Always Love You" was first recorded by Ms. Parton in 1974, it was ineligible to be song of the year. 'You Never Get Tired'

For sheer numbers, the year's other awards were dominated by "Aladdin." Its theme song, "A Whole New World," sung by Peabo Bryson and Regina Belle, won as song of the year and as pop performance by a duo or group; material from this Disney movie soundtrack also won three other awards. Its composer, Alan Menken, won three awards for "Beauty and the Beast" last year and two for "The Little Mermaid" in 1991. "You never get tired of these," Mr. Menken said from the stage.

Scattered through the 79 Grammy categories were two each for the rhythm-and-blues singer Toni Braxton, for the jazz saxophonist Joe Henderson and for the songwriter Sting. Dwight Yoakam, Tony Bennett, Aerosmith, Digable Planets, Ray Charles and Mary-Chapin Carpenter were among the other winners. This year the female rock-vocal category was absorbed by the rock-vocal category, prompting a small protest by a group of women outside Radio City Music Hall. The winner in that category was Meat Loaf. The awards cover recordings released from Oct. 1, 1992, through Sept. 30, 1993.

Backstage, Ms. Houston said she had initially been reluctant to record "I Will Always Love You," which had been chosen by Kevin Costner, who starred in "The Bodyguard" with her. "I'd keep saying, 'This is a country song,' " Ms. Houston said. "But then I starting singing it, and I started liking it."

While the awards for the "Bodyguard" soundtrack were predictable, the ceremony had its anarchic moments. When Bono, the singer of U2, accepted the alternative-music award for the album "Zooropa," he said: "I'd like to give a message to the young people of America. We shall continue to abuse our positions."

He promised to disrupt "the mainstream," using a four-letter word on the live broadcast. Hurt Feelings and an Apology

Bono also introduced Frank Sinatra, who was given a Grammy legends award, with a free-rolling tribute in which he called him, "The big bang of pop," adding, "I'm not gonna mess with him, are you?" Mr. Sinatra followed with a rambling speech, saying he was angry and hurt that he hadn't been asked to sing. The show's band abruptly cut him off; Garry Shandling, the host of the ceremonies, apologized soon afterward. Michael Greene, the president of the National Academy of Recording Arts and Sciences, said after the broadcast that the decision to cut away from Mr. Sinatra had been made by "Frank's own people, not by the show's producers."

Billy Joel, while performing "River of Dreams," paused midsong and intoned, "valuable advertising time going by . . . dollars, dollars, dollars." The song lost to Sting's "If I Ever Lose My Faith in You" in the pop vocal, male category. It was Sting's 11th award, with and without the Police. His album "Ten Summoner's Tales" also won awards for its engineer and as a long-form video. With Familiar Names

The National Academy of Recording Arts and Sciences, whose 7,000 members vote on the Grammy Awards, is famous for its repeat choices. Despite its designation as alternative, U2 had already won five awards, including one for album of the year with "The Joshua Tree." Last night, Mary-Chapin Carpenter won her third award in a row as female country vocalist; the song, "Passionate Kisses," also won the country-song award for its writer, Lucinda Williams.

Pat Metheny won his seventh Grammy in the contemporary-jazz category and B. B. King won his seventh blues award. Natalie Cole won her seventh Grammy Award for jazz vocals. And With New Voices

Some newcomers were honored at the ceremony. Ms. Braxton, who was named best new artist, also won the female rhythm-and-blues vocal award over Ms. Houston and Janet Jackson. Stone Temple Pilots won in the hard-rock category over more established performers like AC/DC and Robert Plant; gangster rap received its first Grammy when Dr. Dre's single "Let Me Ride" took the rap solo award. Digable Planets' combination of jazz and rap won the rap group Grammy.

The ghost of Miles Davis hovered over the jazz awards. Mr. Henderson, the tenor saxophonist who won a Grammy Award for 1992, won for both solo and group performances from "So Near, So Far (Musings for Miles)," a Davis tribute; "Miles and Quincy Live at Montreux," a collaboration by Davis and Quincy Jones, won in the large jazz ensemble category. That gave Mr. Jones his 26th Grammy, second only to Sir Georg Solti, who has 30.

The classical category was dominated by "Bartok: The Wooden Prince and Cantata Profana," performed by Pierre Boulez conducting the Chicago Symphony. The pairing won awards as classical album, orchestral performance, choral work (for the cantata), and classical engineering. Handel's "Semele," conducted by John Nelson, won in the opera category; the Emerson String Quartet won with a chamber music album of Ives and Barber quartets. John Browning's recording of Barber's complete piano works won in the classical instrumental soloist category.

Amid the categories, there was room for everything from polka album to comedy. The poet Maya Angelou picked up the award for spoken word or nonmusical album for the recording of the poem she read at President Clinton's inaugural ceremonies, "On the Pulse of Morning." "Imagine," she said, clutching her award. "Me getting a Grammy!"

Photos: Whitney Houston with her Grammy Award for best pop vocal performance, female; Sting won for best pop vocal performance, male. (pg. C15); Frank Sinatra, left, being congratulated by Bono, the lead singer of the rock group U2, after winning a legends award last night at the Grammy ceremony at Radio City Music Hall. Backstage, Meat Loaf, right, held his award for the best rock vocal performance. (Photographs by The Associated Press) (pg. C22)