The nightclub blasts killed more than 200 people.
In total, 22 countries lost people, but Australia suffered the most losses with 88 citizens killed.
Australian Prime Minister John Howard and leaders from Indonesia, the world's most populous Muslim country, were among those at the service.
"We haven't forgotten you. We never will," Howard said at the memorial.
Chief security minister, Susilo Bambang Yudhoyono, vowed to fight terrorism and said Indonesia would not rest until it had caught all those behind the blasts.
About 40 people have been captured and 20 sentenced, including three sentenced to death.
"They were our sons, our daughters, our fathers and mothers, brothers and sisters, our cousins, our best friends."
Susilo Bambang Yudhoyono,
Indonesian Chief Security Minister
"Never mind your nationalities, never mind your race, religion, or ethnicity or profession," Yudhoyono said. "They were our sons, our daughters, our fathers and mothers, brothers and sisters, our cousins, our best friends."
"Make no mistake that those outstanding suspects will be hunted down," Yudhoyono said. "History will condemn them for ever."
Indonesia has blamed the blasts on Jemaah Islamiah (JI), the Southeast Asian group that the US claims is linked to al-Qaida.
Across Australia, flags flew at half-mast as the country stopped to mark the anniversary.
Australian Prime Minister John
Howard spoke at the ceremony
On a windy cliff top, overlooking Coogee beach in Sydney, 1000 people gathered for the dedication of a memorial at the site renamed Dolphins Point after the Coogee Dolphins rugby
league team, which lost six players.
Some Australian footballers who lost friends in the attacks had the number 88 – the number of Australian victims – sewn onto jerseys. A few relatives clutched photos of loved ones.
Howard then went to the bomb site and placed a floral wreath at a memorial across the road from where the Sari Club once stood, and where the names of the 202 dead have been etched in gold letters on a stone tablet.
Other events will run during the day, finishing with a small Balinese ceremony at the bomb site at 23:08 (15:08 GMT), the exact time that many, holidaying on the lush island paradise were brought to an end one year ago.
Many victims have been drawn to the site where the Sari Club was once a beacon to good times, but is now a shrine where photos of dead loved ones fill a board that stretches the length of the empty lot.
Indonesia's President, Megawati Sukarnoputri, will not attend the day's ceremonies on the island.
Officials originally said Megawati had to receive the visiting Algerian president that day.
But on Sunday morning she was in North Sulawesi at a bridge inauguration.