His parents, Jo and Moe Rayner, were with him when he died at Phoenix Children's Hospital in Arizona, said his sister, Brittany.
Brandon was taken to the hospital in October for bone marrow transplants.
The first transplant was unsuccessful, his family said. Although he underwent a second bone marrow transplant, he was too weak to handle a lung infection, Brittany Rayner, 25, said.
"He couldn't fight it,'' she said.
This past summer, Brandon began his quest to collect the most business cards so that his name could be included in the Guinness World Records.
At the time, he figured he needed to gather more than 150,000 cards. But Guinness officials said there was no number on record for the feat.
By July, Brandon had collected 14,000 cards while undergoing treatment at Sunrise Children's Hospital in Las Vegas. By September, his stockpile had swelled to more than 500,000.
Officials at Sunrise said Brandon counted just over 900,000 cards before his death.
But there are boxes of cards that have yet to be counted, said Ashlee Seymour, a hospital spokeswoman.
"The family is no longer collecting cards at this point,'' she said Tuesday. "They still plan to pursue the record in Brandon's honor."
Jo Rayner said that she submitted the application to Guinness for the record on her son's behalf in September but that she had not heard back from the company.
In a previous interview about her son's quest, Rayner said Brandon always showed a fascination with collecting things. However, she said, "I didn't think it would go this far. Ever since he was 2, he wanted to collect something. But it would only last a short period of time."
As Brandon received business cards, he sorted them into stacks of 100. He would then put those 100 in alphabetical order based on the business name.
He would put some of his favorites in a leather three-ring binder.
In addition to collecting business cards, Brandon inspired others at Sunrise Hospital, said officials, who spoke of him as if he were the hospital's main guest. He was considered quite "bubbly."
"Brandon became a spokesperson and young advocate for blood and bone marrow transplants, and we will continue his mission to encourage those donations," Seymour said. "Brandon meant a lot to the hospital, and we will miss him greatly."
Brandon also was among the first patients to participate in a new classroom for hospitalized children at Sunrise. Through a partnership with the Nevada Childhood Cancer Foundation and the Tourino Foundation, Sunrise has added an education component to the oncology unit for children who must spend a lot of time at the hospital.
A memorial service for Brandon will be held at 2 p.m. Friday at Canyon Ridge Christian Church, 6200 W. Lone Mountain Road, at Jones Boulevard.
Monetary donations can be made to The Brandon Rayner Benefit Fund through the Bank of America.
Donations also can be made to the Nevada Childhood Cancer Foundation and Candlelighters Childhood Cancer Foundation of Southern Nevada.
Besides his parents and sister Brittany, Brandon is survived by brothers Chris, 24, A.J., 23, and Marcus, 21
