Among Taylor Swift’s prizes were best female artist, best streaming song for Shake It Off and the ceremony’s top honor, artist of the year.
Sam Smith won best new artist – and accepted his trophy using flash cards after having vocal surgery.
Kanye West was booed as he closed the show with a medley of hits.
Audience members jeered as Kanye West’s sisters-in-law, Kendall and Kylie Jenner, introduced his set; and the booing continued during his performance.
Surrounded by pyrotechnics and largely in the shadows, Kanye West’s delivery on All Day and Black Skinhead was angry and intense. And while some disapproved, other fans could be seen pumping their fists to the tracks.
TV audiences were also left mystified as the first minute of his set was censored by broadcasters ABC – reminiscent of Kanye West’s performance at the Brit Awards earlier this year.
Other artists were more favorably received, with Britney Spears and Iggy Azalea receiving a standing ovation for the first performance of their new song, Pretty Girls.
Simple Minds took to the stage to perform Don’t You Forget About Me, marking the 30th anniversary of teen movie The Breakfast Club, which featured the song in its closing moments.
One Direction came away with two trophies, for best group and best touring artist, dedicating the latter to “our brother Zayn” Malik, who left the band in March.
Taylor Swift opened the show with the premiere of her star-studded new video, Bad Blood – which features the likes of Ellie Goulding, Selena Gomez, Jessica Alba and Cindy Crawford.
The singer, who has successfully transitioned from country artist to pop star, accepted the prize for best album by thanking the fans who “embraced change”.
“I love you so much, more than I will be able to say to you,” Taylor Swift said.
Sam Smith, who is recovering from throat surgery, sent his acceptance message in a special video.
He held up a series of cards, reading: “Thank you Billboard for this incredible honor. Secondly, thank you to my amazing fans. It’s times like this that I realize how lucky I am to have you in my life.
“I can’t wait to get this surgery out of the way so I can sing my ass off for you again.”
Iggy Azalea won top rap song for Fancy, her collaboration with Charli XCX, while John Legend won Top radio song for All Of Me.
Meghan Trainor’s All About That Bass was named top digital song and top Hot 100 song, recognizing its US chart performance.
Coldplay won best rock album for Ghost Stories, while Irish singer Hozier picked up best rock song for Take Me To Church.
In tribute to the late singer Ben E King, rock band Imagine Dragons performed Stand By Me to an audience that included the late singer’s daughters and granddaughters.
Presenter Ludacris also gave a touching tribute to blues star BB King, who died on May 15.
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