Many left flowers and lit incense at his grave in Lake View Cemetery, Seattle, on Monday.
And there were also several events to mark his death in his home town of Hong Kong and the village where his parents were born in China.
Lee died of a swelling of the brain in 1973 at the tender age of 32.
He passed away in Hong Kong a month before his Hollywood debut, Enter the Dragon, was released in the US.
Kung fu master
He is widely admired as a great kung fu master who popularised the martial art and made it accessible to western audiences.
One fan, Michael Seeder, 29, of Portland, Oregon, said: "He never let anything stop him. He never put limitations on himself. If an obstacle got in his way, he found a way around it."
Taky Kimura was Lee's best man at his wedding to Linda Emery. The 79-year-old said Lee was a man determined to convince people they could do great things if they stayed true to themselves.
"I think so many of us get wrapped up trying to be like someone else, when the beauty is within yourself," he said.
The cemetery's manager, George Nemeth, said five or six people turned up most days to ask about Lee's grave, while others found it themselves.
Broke racial barriers
Lee's widow, now called Linda Lee Caldwell said she was proud of the barriers her husband broke through - whether racial, economic or physical.
"Everyone can relate to having limitations in life and Bruce is an icon to them in overcoming those limitations," she said.
Born in San Francisco in 1940, Lee grew up in Hong Kong, then returned to the United States when he was 18.
He lived in Seattle for over 4 years in the early 1960s where he opened his first kung fu studio while studying philosophy at the University of Washington.
He fell in love with one of his students, Linda Emery, and they married in 1964.
All-time great film star
Lee first became known to US audiences as Kato, a sidekick in the 1960s television series, "The Green Hornet."
He acted in a series of Hong Kong films in the early 1970s, which made him a star in Asia, then Europe and eventually the United States.
His Hollywood debut came in 1973 with "Enter the Dragon," a box office success he never lived to see.
A black-and-white picture of Bruce Lee is set in the red granite of his tombstone above his name, etched in gold lettering.
A shiny, jet-black slab jutting from the base of the headstone reads: "Your inspiration continues to guide us toward our personal liberation."