Yes. If you have reason to believe they didn’t know better and you’re feeling generous, try to email them directly and tell them they have four hours to remove the stolen content before you file a formal DMCA takedown notice.
(I have a more detailed article on the DMCA takedown process here. )
And for the record, it’s absolutely NOT TRUE that you can’t do anything if they give you credit.
When you create and publish original content, whether it’s in the form of text, images, video, or audio, you own that content under the law and have full rights to control where and how that content is used.
The only exceptions are that someone can quote a small portion of your text or use a thumbnail image for educational or other limited non-commercial purposes. They may also be able to parody your work. There are no 100% hard and fast rules as to how many words they can post, but you can find guidelines at U.S. Copyright Office or Plagiarism.org or consult with an attorney if you’re interested in learning more.
You are only required to file for a formal copyright if you plan to sue an infringer, but it’s not a bad idea to file for content that you value.
If your articles were stolen by websites that publish infringed content on a regular basis, first file takedown notices with Google. My article referenced above gives you the link for that. This will make their version of your article disappear from Google. Then file your takedown notice with the host.
If you can’t find out who the host is, they may be hiding behind a service like Cloudflare. In that case, file a notice with Cloudflare and they will respond with information about the true host. Then you can file with that host.
If it turns out that the host is in another country, it’s possible that you may only be able to remove them from Google search results, but that’s better than nothing.
There are times you might not want to force someone to remove your content; if they only post a small portion of your article and link back to your site, they might be doing you more good than harm. But that’s usually the exception.
One reason that you should force infringers to remove your content is that you may end up with a “duplicate content” penalty from Google. This is thought to not be as much of a problem as it was once thought to be, but if you’re putting hard work into creating your own content to grow your website traffic, don’t take that chance.
One example of why people should enforce their copyrights is this: I have a client who does auto body repair, and when his photos are stolen to use on other auto body repair sites, it can make potential clients think his photos are not original before and after shots of his own work. But they are. This can damage his reputation, so we get them removed immediately when we find them on other sites without permission.
So, yes. In most cases, you should do something to protect your property. All the instructions are posted on the article I added the link for, and after you send one notice you can use that as a template to send others if needed.
EDIT: As David Thomas pointed out, if you voluntarily post your content on a website that you do not own/control, you may be subject to their terms. You even have to be careful using Google Drive, for example, because if you make an image public, their terms (which you accept automatically when you use their service) allow them to use that for advertising, and that’s been an issue with Facebook, too. But rarely would those terms allow others to use your content without your explicit permission. The only exception I can think of is when sites like YouTube offer embedding. And even there you can disable embedding of your videos.
So always read the terms of service when you post content to a site you don’t own, and consider adding your own terms of service to your site to spell out what you do and do not allow others to do with your work.