Police in Portland accused some demonstrators of carrying bats and arming themselves with stones. Objects were thrown at the police, who responded with pepper spray and rubber baton rounds.
Protesters in the city centre could be heard chanting "We reject the president-elect!"
Spencer and Kristen Foxworth, who left the protest before it turned violent, told the BBC most of the demonstrators were just ordinary people like themselves who were horrified by some of the things Mr Trump stood for.
"This is not any sense of a hangover, this is more like the galvanising effect," Mr Foxworth told Outside Source. "People who were quiet, were polite or not activists by any means - I mean myself, for example - are now galvanised by this. Trump now has the Senate and the House, and there will be very little checks and balances on his actions."
There were no reports of violence at the other protests:
Demonstrators in Minneapolis briefly blocked an interstate highway in both directions
In Philadelphia, crowds gathered near City Hall holding placards bearing slogans such as "Not Our President", "Trans Against Trump" and "Make America Safe For All"
In Baltimore, police say a peaceful crowd of 600 people marched through the city, blocking traffic
In San Francisco, high school students waved rainbow banners and Mexican flags
A small crowd also gathered outside Trump Tower in Chicago while protesters also returned to Trump Tower in New York for a second night
Senior Trump adviser and former New York mayor Rudy Giuliani, tipped by some to be the next attorney general, called protesters on college campuses "a bunch of spoiled cry-babies".
Republican National Committee chairman Reince Priebus said anti-Trump protesters had to accept the election results.
"Everyone needs to just take a deep breath, take the weekend... count our blessings, and let's come back on Monday," he told ABC News.
Mr Trump's team is understood to be focused on quickly filling key national security posts.
Kind words will be hard to come by for Hillary Clinton for a while. She just suffered an ignominious defeat at the hands of a man she considered little more than a pest right up until the state of Florida kicked her in the pantsuit. But I’m not here to gloat. Gloating is unsportsmanlike, and gloating over beating a girl is exceptionally bad form. It’s possible my parents might read this, and they think they raised me better than that. So instead, I come to thank Hillary Clinton, not punish her. And we all owe her a massive debt of gratitude.
So, I’ll say it: thank you, Hillary. Thank you for running a campaign so beset by scandal and marred by duplicity divisiveness that it made President Barack Obama look like President Ronald Reagan. Eight years of Obama’s ugliness have left Americans giving each other the side-eye like the Hatfields and the McCoys. You needed to run a delicate, almost surgical campaign to keep from getting absorbed by the general din of Democrats’ hate machine. Instead, you brought a chainsaw.
Thank you for not only cheating Senator Bernie Sanders out of a shot at the title, but doing it with such complete disregard for your own party apparatus that you alienated millions of likely voters in the process. Not one, but two DNC chairpersons laid down in traffic for you and you treated them like human sandbags. And you made almost as much effort hiding your game-fixing as you did hiding your disdain for dissent from “the little people.” I haven’t seen breakdowns on how many otherwise committed “progressives” decided to stay home on Election Day and reread The Motorcycle Diaries, but I bet it was more than a few.
Thank you for promising to continue the Obama legacy. Even as the soon-to-be-ex-President’s “signature accomplishment” Obamacare began its last lap around the toilet bowl, you swore to keep it on life-support, even reminding everyone that your “Hillarycare” was partially responsible for the monstrosity. You kept trying to serve that crap sandwich no matter how many times we sent it back to the kitchen. Trump’s opposition to Obamacare was predictable, and unlikely to sway anyone not only already appalled. But you told people who were suffering that they would find no friend in you.
Thank you for sticking to your guns on Benghazi. Forget about your decision to blame some obscure video which looks like it was shot on a borrowed home camera during lunch break. It was your steadfast refusal to even once offer an unqualified apology for the murders of four good men — one of whom you called a friend — at the hands of terrorists you won’t even identify. Trump could have questioned whether you have a soul from now until your husband’s Viagra prescription ran out, but — to borrow one of your phrases — what difference would it make? You even publicly called Patricia Smith a liar. Only you could make America question your humanity, and oh Lord, did you ever.
Thank you for refusing to come clean about your email. Even after FBI Director Comey told us that he was letting you off the hook — again — you kept behaving as if your multi-year pattern of arrogance and abuse was somehow exempt from scrutiny. You even tried to frame the Russians for creating the issue, as if the KGB forced you to let vital national secrets run through bathrooms, basements and Anthony Weiner’s laptop. But you never owned up to it, and you never really apologized. Only you could lie through your teeth so brazenly, you made up people’s minds for them.
Thank you for using your posting as Secretary of State to help Obama design the dumbest foreign policy since Neville Chamberlain traded Europe for a piece of paper. As the world burned, you ran weapons to ISIS, made backroom deals with the Russians and even paid Iran — the world’s heavyweight champion of supporting terrorism — to accelerate their nuclear weapons program.
Thank you for reminding us that the politics of ignorance, division and hate don’t deserve our support. When you told a national debate audience that you were proud to call the “Republicans” your enemies, you told nearly 50 percent of us that there was no room for us in your America. And then you went out and proved it with a campaign that sounded like it had been lifted out of the Vagina Monologues.
Thank you for running attacks on Trump which were bound to backfire. When you tried to link him to Russia, you reminded us of your role in selling American uranium to Putin’s gang. When you questioned his treatment of women, you reminded us that you rode a serial rapist’s coattails to the political top floor. When you questioned Trump’s wealth, you reminded us of the sketchy-at-best sources of the nine-figure pile you built, despite being so recently “dead broke.”
A couple of weeks back, I lambasted the GOP for offering Trump as a nominee. I didn’t think he had what it took to take the White House. But thanks to your efforts, I needn’t have worried. On behalf of a grateful nation, and a grateful world, I salute you.