Dozens of people have been arrested in the United States after a day of protests in cities around the world where tens of thousands gathered to rally against what they see as corporate greed.

About 175 protesters who were part of a growing anti-Wall Street movement were arrested in Chicago when they refused to take down their tents and leave a city park when it closed, police said.

Police say that 46 people were arrested for criminal trespassing in Phoenix.

The arrests were mostly peaceful and came as somewhat of a contrast to many demonstrators elsewhere, who have taken care to follow laws to continue protesting at Wall Street's role in the financial crisis and other grievances.

Most of the marches were largely nonconfrontational, though dozens were arrested in New York and elsewhere when police moved to contain overflowing crowds or keep them off private property. Two officers in New York were injured and had to be taken to hospital.

At least one protest grew violent. In Rome, rioters hijacked what had been a peaceful gathering by tens of thousands and smashed windows, tore up sidewalks and torched vehicles.

Repair costs were estimated at €1m, the mayor said. Around 70 people were injured.

In Chicago, about 500 people set up camp at the entrance to Grant Park after a protest earlier in the day involving about 2,000.

Police said they gave protesters repeated warnings after the park closed at 11 pm and began making arrests when they refused to leave.

Officers also asked protesters to take down their tents before beginning to cut them down to clear the area, police said. Protesters who were arrested could face fines for violating a municipal ordinance.

The arrests signify a new phase of civil disobedience for Chicago's wing of the movement, organisers said.

"It was very much a choice and calculated," said Randy Powell, a 27-year-old student at the School of the Art Institute of Chicago who was among those arrested. "I feel like I had to."

The tactic to occupy a city park has been used in other places with city officials often working to accommodate the protesters.

In Arizona, reporters and protesters saw an estimated 40 people detained around midnight at a park in Phoenix, and police said some protesters were arrested after they remained in a Tucson park after the closing time.

In New York, two dozen were arrested when demonstrators entered a Citibank branch and refused to leave, police said.

Earlier, as many as 1,000 demonstrators also paraded to a Chase bank branch, banging drums, blowing horns and carrying signs decrying corporate greed. A few went inside the bank to close their accounts, but the group didn't stop other customers from getting inside or seek to blockade the business.

The day culminated in an event in the city's Times Square, where thousands of demonstrators mixed with Broadway showgoers, tourists and police to create a chaotic scene in the midst of Manhattan.

"Banks got bailed out, we got sold out!" protesters chanted from within police barricades. Police, some in riot gear and mounted on horses, tried to push them out of the square and onto the pavements in an attempt to funnel the crowds away.

In New York City, the protesters at the heart of the Occupy Wall Street movement were planning a day of rest today.

Throughout the US - from several dozen people in Jackson, Mississippi, to some 2,000 each in Pittsburgh and Chicago - the protest gained momentum.

Nearly 1,500 gathered for a march past banks in central Orlando, Florida. Hundreds marched on a Key Bank branch in Anchorage, Alaska, and declared it should be foreclosed.

In Colorado, about 1,000 people rallied in central Denver to support Occupy Wall Street and at least two dozen were arrested.

In Canada, demonstrators gathered in cities across the country from Halifax, Nova Scotia, to Vancouver, British Columbia, with hundreds of people protesting in the heart of Toronto's financial district. Some protesters spent the night at parks in Toronto and other cities.

Overseas, tens of thousands nicknamed "the indignant" marched in cities across Europe, as the protests that began in New York linked up with long-running demonstrations against government cost-cutting and failed financial policies in Europe.

Protesters also turned out in Australia, Asia and South Africa.