Organisers said the marches were among the largest in the recent wave of protests against the killings of black males by police in Ferguson, Missouri, New York, Cleveland and elsewhere.
The protests were mainly peaceful, although police in Boston said they arrested 23 people who tried to block a highway.
One person was arrested in New York after two officers were assaulted by protesters, prompting a condemnation from Mayor Bill de Blasio who said the alleged assault marked "an ugly and unacceptable departure from the demonstrations thus far."
"Those who reject peaceful protest and provoke violence can expect immediate arrest and prosecution," warned de Blasio, who has been sharply criticized by the police union for not supporting the department.
Police in Oakland, California, ordered hundreds of demonstrators to disperse on Saturday night after a grocery store was looted.
Decisions by grand juries to return no indictments against the officers involved in the deaths of Michael Brown in Missouri and Eric Garner in New York have put police treatment of minorities back on the national agenda.
"We're going to keep the light on Mike Brown ... on all of the victims. The only way you make roaches run is to keep the light on," said civil rights leader the Rev. Al Sharpton, whose National Action Network organized the Washington rally.
Sharpton urged Congress to pass legislation that would allow federal prosecutors to take over cases involving police violence.
Protesters from around the country gathered at Freedom Plaza, a few blocks from the White House, then marched down Pennsylvania Avenue to rally near the white-domed U.S. Capitol.
Marchers, who included many parents with children, chanted "No justice, no peace, no racist police" and "Hands up, don't shoot." Protesters carried signs that said "All men are created equal" and "Black lives matter."
The Washington protest included relatives of Eric Garner and Akai Gurley, killed by New York police; Trayvon Martin, slain by a Florida neighborhood watchman in 2012; Brown and others.
"What a sea of people," said Brown's mother, Lesley McSpadden. "If they don't see this and make a change, I don't know what we're going to do."
In Missouri, a prosecutor on Saturday made public documents related to the probe into Brown's killing, saying his office had inadvertently held them back.
Protesters gathered in a one-block section of Pennsylvania Avenue and nearby public space, although organizers estimated the crowd at 40,000 to 50,000 people. A police spokesman declined to provide a crowd estimate, citing department policy, and said there had been no arrests.
After the rally, some protesters marched through downtown Washington, briefly closing some streets, police said.
In Boston, a march with hundreds of protesters passed by at the Suffolk County jail near an entrance to Interstate 93. Inmates cheered and banged on cell windows as protesters passed.
Protesters tried to push through police lines near the highway entrance. Massachusetts State Police said 23 people were arrested for disorderly conduct.
The New York march drew a mostly young, ethnically diverse crowd that was loud and peaceful and headed north up Manhattan's Fifth Avenue from Washington Square Park.
Protesters chanted "How do you spell racist? NYPD" and some taunted police guarding the march route.
At the end of the march, protesters raised their hands in mock surrender outside police headquarters in lower Manhattan.
Observers estimated the march size at 20,000 to 30,000 protesters. Police gave no estimate and reported no arrests.
"The culture in America is embedded in slavery, in the courts and the politics, and the culture has to change," said marcher Kayode Leonard, 33, from Manhattan.
In Berkeley, California, scene of ongoing protests, body-sized cardboard effigies of lynching victims were seen hanging by nooses on Saturday at the University of California, Berkeley.
Spokeswoman Claire Holmes said all were taken down. "It has been unclear to us whether this was racially motivated or part of the protests," said Holmes, adding there were no suspects.
