Elsewhere, there was plenty of trouble. Rival marches by opposing groups vying for power took place in Venezuela and France. In Berlin, hundreds of police officers rushed a 5,000-strong crowd of rock fans.
About 10,000 anti-globalisation protesters stormed through London's exclusive district of Mayfair. Business and shop windows were boarded up in advance of the "May Fayre."
In Sydney, Australia, hundreds of demonstrators took advantage of May Day to approach the offices of a company that runs asylum-seeker detention centers. They were beaten back by police on horseback.
In South Korea, 10 major cities were blocked by tens of thousands of trades unionists, while riot police in the Philippines tried to stop the supporters of ex-president Joseph Estrada from getting into the presidential palace.
May 1 is a date now firmly fixed on the calendar for anti-globalisation protests around the world.
What was so astonishing about the comparative calm in the Baltics, where only a handful of demonstrations against this and that were reported, was how insular it showed society in the three Baltic countries to be.
It showed that the Baltics are sometimes an exception to the driving force of globalisation.
The number of people in the Baltic countries who care passionately about the causes that inspire anti-globalisation protesters - environmentalism, animal rights, child labor, third-world debt, the economic domination of multinationals - can be counted on one hand. It would be wise to hold the World Economic Forum and annual meetings of the IMF and World Bank here, away from disruptive crowds.
It's the lack of awareness about these issues in the Baltic countries that is astonishing. For almost everyone, any talk of anti-globalisation is linked bluntly to anti-capitalism and becomes a throwback to the not-so-distant days of the Soviet Union.
Much of the fault lies with the media, which still report on the who, where, what and how of not just the annual May Day disturbances but all global events - and not on the why.
This year, because May 1 has just returned as a state holiday in Lithuania, all three Baltic states took the day off together for the first time since regaining independence from the Soviet Union. But how many people around the Baltics were actually aware of that?