Around 35,000 spectators packed the Stadio Olimpico to watch the two-hour ceremony, that was followed by a worldwide audience of around two million.
The Olympic flame was lit by Italian cross-country skiier Stefania Belmondo, 36, who is Italy's most successful winter Olympian.
Italian President Carlo Azeglio Ciampi officially launched the Games, which promise 17 days of snow and ice sports.
International Olympic Committee President Jacques Rogge told athletes from around 80 countries that they are "role models" and their "conduct will inspire and motivate future generations".
"Our world today is in need of peace, tolerance and brotherhood," Mr Rogge said.
"The values of the Olympic Games can deliver these to us. May the Games be held in peace, in the true spirit of the Olympic Truce."
In an illustration of his words, Cold War foes South and North Korea marched together in a show of unity, with South Korean speed skater Bora Lee joining with figure skater Han Jong-In from the North as they entered the stadium.
It was the first joint march of its kind at a Winter Olympics.
Organisers delivered an event they had earlier described as filled with "Rhythm, Passion and Speed", showcasing Italian culture and history.
Italian tenor Luciano Pavarotti, former top model Carla Bruni, actress Sophia Loren and designer Giorgio Armani are all taking part.
Pavarotti moved the crowd with an emotional rendition of Nessun Dora.
The extravaganza began with music and light as Italian gymnast Yuri Chechi swung a huge hammer onto a bronze anvil, followed by dancers and skaters with red flames emanating from their helmets.
Creative director Marco Balich, earlier said the flames from the inline skaters, dubbed the Sparks of Passion, were chosen to show the speed with which Italians love to live.
The five Olympic rings were unveiled as 2,500 athletes from around the world paraded through the stadium.
Dancers dressed in white sported balloon-like giant bubbles.
Italian culture was then explored, travelling from Dante's Divine Comedy through the excesses of a Renaissance and Baroque feast, followed by a giant sun and moon floating over the stage to represent the quest for knowledge.
A Ferrari Formula One car appeared, in a nod to Turin's car-manufacturing past.
After 28 acrobats formed a white dove above the stage, tribute was paid on the 25th anniversary of John Lennon's death by a call for peace from his widow Yoko Ono, with Peter Gabriel singing Imagine.
Competition gets underway on Saturday, when four gold medals will be awarded in biathlon, nordic combined, women's freestyle moguls and men's speed-skating.
Italy last hosted a Winter Olympics in 1956, and also hosted the 1960 Summer Games in Rome.