Protestors from opposing camps pelted stones and bottles at each other with as many as 2,000 police officers brought in from around the country to separate the two sides.
Leipzig police said about 5,000 people burnt garbage bins and blocked city streets to prevent 550 neo-Nazis from a protests march, leading to the arrest of 20 people.
Another 40 people were arrested in the northeastern city of Rostock, when a fracas broke out between about 500 members of Germany’s extreme right National Democratic Party and 4,000 counter-protestors.
In Germany neo-Nazi demonstrations often provoke much larger counter protests and end in clashes with the police, particularly on May Day.
30 arrested in Chile protests
During the traditional May Day march in Chile, police used water cannon and fired tear gas to disperse youths who broke shop windows and tried to overturn barriers in front of the presidential palace.
At least 30 people were detained and two photographers and a police officer were injured by stones thrown at a mobile television truck.
The mayor of Santiago, Victor Barrueto, condemned the violence and said those responsible would be prosecuted.
In what began as a peaceful march, demonstrators including parents with young children, passed before the presidential palace when youths pushed over palace-protecting barriers, inciting further acts of unrest.
Police estimate about 10,000 people attended the march, organised by the country's main trade union. The union had coordinated with authorities prior to the rally in a bid to prevent violence.
Turkish riot police
Turkish riot police arrested 85 people as scuffles erupted in May Day rallies in three cities, including the capital Istanbul.
The Anatolia news agency has reported that 34 people were taken into custody in Istanbul with television footage showing protestors resisting arrest by hitting officers with sticks.
Police retaliated and fired tear gas and used truncheons as they police descended on left-wing demonstrators who tried to hold a rally at a venue banned by authorities.
According to the news reports, some protestors were injured in the scuffles that broke out in Taksim Square, the heart of the shopping and entertainment district on the city's European side.
May 1 demonstrations have in the past led to violent clashes between security forces and protestors in Turkey.
In 1996, three protesters were killed in Istanbul and dozens of demonstrators and police officers were injured after violence erupted at Kadikoy.
The deadliest May Day in Istanbul was in 1977, when 37 protesters were killed in Taksim Square in clashes with police.
Global protests
In Russia an estimated one million workers were joined by staunch Soviets, who took to the streets across the country to protest against low wages and poverty.
"The industry is in ruins, the salaries are miserable, and working for a living does not provide enough to buy an apartment in a Moscow suburb," said Ivan Klyuchenko, a 17-year-old member of AKM, a group of young communists.
French unions, flushed with success after defeating a new labour law last month, held large rallies around the country.
The unions wanted to keep the heat turned on the weakened government to make further concessions.
In Spain, several hundred farm laborers targeted the rich to underscore their grievances.
The workers briefly occupied the sprawling estate of the Duchess of Alba to protest that 80 percent of European Union farm subsidies go to the 30 largest landowners in the southern Andalusia region, according to union organisers.