Swift's five awards included artist of the year, beating Michael Jackson, who made history from beyond the grave by winning four awards. His awards included favourite rock or pop artist, bringing his career total at the event to 25.
His sister Janet opened the event with a medley of his songs. Brother Jermaine collected an award on his behalf.
Swift also paid tribute to Jackson in her speech.
"Music has ultimately never been about competition," she said as she accepted the top prize over a satellite link from London, where she performed yesterday.
"To even be mentioned in a category with Michael Jackson is an unimaginable honour."
Lopez was reported to be "fine" after a fall on her famous derriere during a tricky dance move.
Performing her latest single Louboutins, Lopez climbed a pyramid of half-naked male dancers, lost her balance and fell on her bottom. But she quickly recovered and went on with the show.
Former American Idol contestant Adam Lambert also had a fall during his raunchy performance.
Houston, 46, received the International Award of Excellence for her musical and philanthropic work, and returned to the AMA stage with a performance of I Didn't Know My Own Strength. She dedicated the award to her daughter, to music mogul Clive Davis, and to "everybody who supported me".
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