Television shows are also celebrated at the gala, where prizes are divided between dramas and comedies or musicals.
Cameron's double victory was a vindication of the 55-year-old's faith in his ambitious and costly computer-generated fantasy.
His best director prize also saw him triumph over his ex-wife Kathryn Bigelow, nominated in the same category for Iraq drama The Hurt Locker.
"This is the best job in the world," he said as Avatar was named best film. "What we do is make entertainment for a global audience."
The Canadian film-maker previously won a Golden Globe for directing Titanic, which went on to win 11 Academy Awards in 1998.
But he steered clear of the self-aggrandising language of his "king of the world" Oscar acceptance speech, heaping praise upon Bigelow, and addressing his actors in Na'vi, the language created for his blockbuster film.
As Cameron accepted his prizes, it was revealed that Avatar had remained top of the US box office for a fifth week.
Worldwide takings for the film now stand at $1.6 bn (£979m), setting it on course to top Titanic's $1.8 bn (£1.1bn) haul this week - which would make it the top-grossing film of all time.
I like a drink as much as the next man... unless the next man is Mel Gibson
Streep's win for best actress in a musical or comedy came for her role as TV chef Julia Child in Julia & Julia.
"In my long career I've played so many extraordinary women I'm being mistaken for one," said the 60-year-old, who was nominated against herself in the category.
Bullock, meanwhile, received the best actress in a drama prize for her role in The Blind Side as a Southern mother who adopts a homeless black teenager.
Her victory was a blow to British hopes, coming at the expense of Emily Blunt, Carey Mulligan and Dame Helen Mirren.
British star Colin Firth also went home empty-handed thanks to Jeff Bridges' popular win in the best dramatic actor category.
Golden Globe stars talk about the situation in Haiti
"You're really screwing up my underappreciated status here," joked the 60-year-old as he received his award for country music drama Crazy Heart.
Earlier Robert Downey Jr feigned petulance as he picked up the best comedy actor prize for his title role in Sherlock Holmes.
"If you start playing violins I will tear this place apart," he warned, describing the Hollywood Foreign Press as a "strange bunch" for recognising his work in Guy Ritchie's film.
As expected, comedian and talk show host Mo'Nique was named best supporting actress for her role in hard-hitting drama Precious.
"Thank you God for this amazing ride," she told the audience. "I am in the midst of my dream."
The little-known Christoph Waltz was another expected winner, picking up best supporting actor for his work in Quentin Tarantino's Inglourious Basterds.
Streep paid tribute to her mother as she collected her award
The Austrian actor thanked the Pulp Fiction director for giving him a "dizzying experience".
One surprise recipient was raucous farce The Hangover, which took home the Golden Globe for best musical or comedy.
Pixar film Up, meanwhile, was named best animated feature, winning an additional prize for its original score.
Its success contrasted with that of Up in the Air, which had been expected to win a number of the six awards it was up for.
In the end, though, the George Clooney film only won a single prize for its screenplay.
In the best television actor (mini-series) category, Kevin Bacon beat a quartet of British and Irish nominees - Kenneth Branagh, Chiwetel Ejiofor, Brendan Gleeson and Jeremy Irons - for his role in Taking Chances, a drama about a Marine who escorts a fallen gulf war soldier home.
Other recipients of TV included Dexter star Michael C Hall, who was a popular winner of the best actor in a drama prize.
The 38-year-old recently announced he has been diagnosed with Hodgkin's lymphoma and is in remission from the disease.
While Dexter won an additional prize for supporting actor John Lithgow, it lost the best drama series award to Mad Men.
The comedy or musical prize was won by Glee, which had been up for more awards than any other TV show.
A touch of Hollywood glamour on the red carpet
Elsewhere actors Robert De Niro and Leonardo DiCaprio joined forces to present director Martin Scorsese with a special award for his outstanding contribution to entertainment.
The 67-year-old said it was "humbling" to receive a prize named after Hollywood great Cecil B DeMille.
His rapturous reception contrasted with the lukewarm one given to host Gervais, whose jokes at the expense of Sir Paul McCartney and others did not always find favour with the star-studded audience.
Film trade paper The Hollywood Reporter gave the star a thumbs down, saying he "flew through" his quips "so fast he didn't land a blow, let alone draw blood".
Celebrities were greeted with a heavy downpour as they arrived at the Beverly Hilton, forcing them to seek shelter under umbrellas.
Inside Nicole Kidman was one of several stars to pay tribute to victims of the Haiti earthquake, urging viewers to donate to relief efforts.
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