In the capital, Kiev, about 15,000 people took to the streets, in one of the biggest protests since Ukraine's independence in 1991.
The protests marked the second anniversary of the disappearance of journalist Georgy Gongadze, whose headless corpse was subsequently found in a forest near Kiev - a killing the opposition blames on President Kuchma.
Mr Kuchma rejects all the charges, and instead accuses his critics of trying to undermine what he calls his course of reforming the country before he steps down in 2004.
United in protest
Yellow and blue Ukrainian flags flew next to the red banners of the Communists - an indication, says the BBC's Ray Furlong in Kiev, of the breadth of opposition.
Protesters marched down to Kiev's Europe Square, shouting "Shame! Shame! Kuchma out!" and defying a ban on demonstrations in the city centre.
"Today is a great day for Ukraine. Thousands of people came here to show they do not want to remain slaves," Yulia Tymoshenko, one of the opposition leaders, told the crowd.
Demonstrators also accused the president's administration of censorship, a charge Mr Kuchma has repeatedly denied.
Nevertheless, in what our correspondent said was a strange coincidence, all Ukraine's TV channels went off air several hours before the demonstration in Kiev.
The official reason was that they were undergoing maintenance, and they later resumed broadcasting.
Tens of thousands of people also held rallies in Lviv, Donetsk and other Ukraine's cities.
Weakened opposition
President Kuchma was not in Ukraine, as he was attending an economic forum in Salzburg.
Experts doubt the demonstrations will force his resignation, pointing out that Mr Kuchma survived what many said was the biggest political scandal since Ukraine's independence.
The scandal - dubbed Kuchmagate - was triggered by leaked tape recordings in which he was allegedly heard calling for Mr Gongadze to be got rid of.
Experts also say opposition is somewhat weakened by the ambiguous position of its most popular figure, Viktor Yuschenko, who joined the protests, but also called for dialogue with the president.