At that moment, Cameron did seem to be master of all he surveyed. After a decade of hits - The Terminator (1984), Aliens (1986), Terminator 2 (1991) and True Lies (1994) - Titanic was merely the latest Cameron box-office behemoth to crush everything in its path.
And yet, in the following eight years, tumbleweed has blown through Cameron's movie CV. What happened to the king of the world? What has become of the director whose movies kept studio bosses in diamond-studded Jacuzzis? Is he just sitting at home counting his money?
The answer is that Cameron, who hails from a remote part of Ontario, has been living up to the other famous phrase he has used to describe himself - "a nerd from Kapuskasing" - and pursuing his passion for scientific documentaries, spending a large chunk of his reputed $50m fortune on educative factual films. His latest documentary, The Exodus Decoded, is screened on the Discovery Channel this Saturday.
The big news is that Cameron is gearing up for a grand return to movies. He has started work on Avatar, a special effects-led feature film about a human who's put in charge of an alien planet.
"I felt I'd exhausted the treasury and it was time to go back to work," Cameron says. "Avatar is a very ambitious sci-fi movie." The director's enthusiasm is evident in his voice. "It's a futuristic tale set on a planet 200 years hence. It's an old-fashioned jungle adventure with an environmental conscience. It aspires to a mythic level of storytelling."
Avatar is not entirely a new venture; Cameron wrote the screenplay 11 years ago, and it has featured on Empire magazine's list of the 12 greatest unproduced scripts in Hollywood.
"I was never bored of making features," the director says. "This has been a dream project of mine for more than a decade, but when I first wrote it, the technology was not advanced enough. So I stuck the script in the drawer until the technology caught up."
Now it has. "The film requires me to create an entirely new alien culture and language, and for that I want 'photo-real' CGI characters. Sophisticated enough 'performance-capture' animation technology is only coming on stream now. I've spent the last 14 months doing performance-capture work - the actor performs the character and then we animate it.
"We've set up a studio, and last week [Lord of the Rings director] Peter Jackson and Steven Spielberg were here trying out the technology. I said to them, 'Take my tools and play with them for a week.' They were grinning from ear to ear. It's a really exciting time because so many new things are now possible."
For all that, Cameron stresses that movies should ultimately be about the story. "Film-making is not about sprockets. It's about ideas, it's about images, it's about imagination, and it's about storytelling."
Now 52, the director is a grizzled figure with more than a touch of the sea dog about him. Five times married, he possesses an effortless authority. Nicknamed "Iron Jim", he has been described as a harsh taskmaster by some colleagues. Others, however, argue that it is this very perfectionism that has helped the director to create some of the most memorable movies of the past two decades.
Cameron contends that "a director's job is to make something happen, and it doesn't happen by itself. So you wheedle, you cajole, you flatter people, you tell them what needs to be done. And if you don't bring a passion and an intensity to it, you shouldn't be doing it."
Cameron is fired up about going back to movie-making. But that does not mean he feels the last decade has been wasted - quite the contrary; he's devoted the same ardour to documentaries as he did to feature films.
The captivating factual programmes he has made include Ghosts of the Abyss and Last Mysteries of the Titanic, films that used state-of-the-art submersible technology to probe uncharted corners of the wreck of the great liner that went down after hitting an iceberg in 1912.
Cameron has also dived to the bottom of the Atlantic in the company of two German survivors to explore the remains of Hitler's flagship, the Bismarck. For the director and his two passengers, it was a moving, often tearful pilgrimage. The resulting documentary - Expedition: Bismarck - underscored the enduring impact of the past on the present.
The director says that these factual films have been voyages of discovery both for himself and for his audience. "The wrecks are interesting in and of themselves - as objects, as pieces of engineering - but ultimately they're a doorway into another time. I think of the submersible, when we're doing this wreck diving, as a time machine."
Above all, Cameron is keen to celebrate the work of scientific pioneers. He is, after all, the son of an engineer. "I just want to be a cheerleader for legitimate scientific exploration. I think there's a necessity as a film-maker to help get the message out, whether it's exploration, conservation, or respect for organisms and ecosystems.
"I'm driven by curiosity. I want to know how everything works, from the Big Bang onwards. There are still huge areas of curiosity to fulfil. When you've got a great story, whether it's a feature or a documentary, you've simply got to pursue it."
The latest fruit of his enthusiasm is The Exodus Decoded. Produced by Cameron, the programme follows the presenter Simcha Jacobovici, who, after six years of archaeological research, has concluded that the Exodus described in the Bible actually happened hundreds of years earlier than previously believed. The tale of the Exodus lies at the core of Judaism, Christianity and Islam. Cameron reckons it still strikes a chord. "Exodus is a story we all know. We were all raised with a biblical view of the world, which still has a resounding influence on Western culture.
"Simcha is brilliant at finding new evidence and making cognitive leaps that so-called experts aren't allowed to. Connecting the dots, seeing a pattern in disparate pieces of evidence and lateral thinking are all more the province of the film-maker.
"Here, we've found evidence that may set the Exodus clock back 200 years. We can shove this film in the experts' faces and start a dialogue. History is often told by the victors. It is edited by subsequent rulers, who chisel away at it to show themselves in a better light. History is a moving target, and we should not be afraid to be provocative about it.
"The challenge for documentary-makers is: how can we illuminate history and paint a clearer picture? Look at the Titanic site - steel can't lie. It is what it is. Regardless of what the newspapers said in 1912, the wreck is lying at the bottom of the ocean telling us its own story."
Having not directed a feature film for so long, does the film-maker feel any added pressure? "No. There is always pressure to perform from one feature to the next. There are always high expectations.
"I remember going with a great sense of anticipation to each new Stanley Kubrick film and thinking, 'Can he pull it off and amaze me again?' And he always did. The lesson I learnt from Kubrick was, 'Never do the same thing twice.' Avatar is not like anything else I've done - nor were Titanic or Terminator or Aliens.
"I always want to find something mentally engaging. I'll spend many months completing the special effects on Avatar, and it will not be released until the summer of 2009. It's quite a challenge - and for that reason, I embrace it."
'The Exodus Decoded' is on Saturday at 9pm on Discovery Channel
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