Protesters shouted "democracy" and waved banners criticising planned changes to laws on surveillance.
The measures would expand government access to digital data and allow for greater surveillance by police.
The EU is investigating whether the new legislation violates its standards.
The conservative Law and Justice Party was elected with a majority last October - the first time since democracy was restored in 1989 that a single party won a mandate to govern alone.
"We want to keep our democracy and freedom," one of the organisers said.
"Our privacy, intimacy is under threat, we can be followed, watched over both in our homes, and online," Mateusz Kijowski, leader of the Committee for the Defence of Democracy, told the protesters.
One banner carried in Warsaw read: "You're supposed to listen, not listen in."
Another sign said "Happy New Year 1984", an apparent reference to the authoritarian state portrayed in George Orwell's novel 1984.
In Warsaw, the estimated 10,000-strong crowd gathered in front of the office of Prime Minister Beata Szydlo before marching to the palace of President Andrzej Duda.
The EU is carrying out a preliminary assessment of whether curbs to the power of the constitutional court and moves to put public media under government control violate the bloc's principle of the rule of law.
Ms Szydlo told EU lawmakers this week that her government had not breached EU or Polish laws and had a mandate to overhaul the country's laws.

Turkey midfielder Turan slotted in the first goal at the Nou Camp from Messi's through pass in the 10th minute.
Barcelona goalkeeper Claudio Bravo then saved Vicente Iborra's penalty after Samuel Umtiti handled.
Turan chipped in his second shortly after the break, with Messi guiding in a sublime header for the third.
It is the first time Barcelona have won the Spanish Super Cup since 2013.
The two-legged match usually pitches the league champions against the Copa del Rey winners. However, as Luis Enrique's team won both trophies last season, Sevilla took part as Copa del Rey runners-up.
Both sides begin their La Liga season on Saturday, with champions Barcelona at home to Real Betis, while Sevilla, who finished seventh last May, host Espanyol.
Thousands of Poles have taken part in marches in Warsaw and other cities to protest about plans of the conservative government, which they say will curtail privacy and freedom.
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Arda Turan scored twice and Lionel Messi once as Barcelona earned a 3-0 second-leg victory over Sevilla to win the Spanish Super Cup 5-0 on aggregate.