Unionist rallies were held all over Spain
Major demonstrations are being held in many European countries to mark international labour day.
Trade unionist marchers have been joined in some cities by anti-war protesters and supporters of other causes.
Fears of anarchist violence in the UK had gone unrealised by late afternoon though there were overnight clashes in Germany.
Opponents of pension reforms took to the streets in France and Austria, while eurosceptics protested in Sweden and the Czech Republic.
The BBC's Ray Furlong in Berlin says that a number of anarchists were arrested in the early hours, but several thousand union activists later marched peacefully through the city.
He says speakers at a union rally condemned economic reforms proposed by Chancellor Gerhard Schroeder, accusing him of dismantling the welfare state and betraying his Social Democrat principles.
Mr Schroeder himself came out to defend the reforms at a rally in the state of Hesse.
"Whoever believes that it's enough to cling to tradition misjudges the challenges," he told the mostly trade unionist crowd, which responded with boos and whistles.
The far-right NPD party also marched through part of Berlin.
More anarchist marches are taking place, and our correspondent says there is a fear of more violence at the main one in Kreuzberg district where traditionally most May Day disturbances occur.
In the Greek capital Athens, thousands took to the streets in two separate marches by communists and trade union groups, both towards the US embassy.
Marchers chanted anti-US slogans and carried banners saying "work, not bombs" and "no to the occupation of Iraq".
Peace protesters unfurled a huge flag in Vienna
Spain's two main trade unions marched in several cities under one banner: "For peace, for work. No to war."
One union leader Jose Maria Fidalgo was carried bleeding from the Madrid rally after being hit on the head by a placard.
In Turkey it is reported that some 30 left-wing protesters have been arrested in Istanbul, at what authorities described as an "illegal" rally.
The NTV television channel showed officers hitting protesters with truncheons and dragging one away by the hair.
An authorised rally by trade unions was also planned in Istanbul, and in other Turkish cities.
In Moscow, Russia, around 15,000 people turned out for the traditional Communist Party May Day march, while rival rallies organised by the pro-government United Russia bloc and the centre-right Union of Right-Wing forces were reported to have attracted 25,000.
The day began with a rally in support of the leader of the radical National Bolshevik party, the writer Eduard Limonov, who was sentenced to jail last month for illegal possession of arms.
In Norway demonstrators are opposing the US presence in Iraq and the Israeli occupation of Palestinian territories.
In Sweden the Left Party is calling on Swedes to reject a propsal to join the euro currency in a referendum on 14 September - though an equal number of demonstrators turned out to support the pro-EU Social Democratic Party.
In Switzerland protests are focusing on support for women's rights.
In Paris, far-right National Front leader Jean-Marie Le Pen drew a smaller crowd than a march last year ahead of his presidential challenge to Jacques Chirac.