Go to "Edit" -> "Paste Special..." and choose "Unformatted text." Should handle it.
If not, paste it into a TXT file first. That's a good way to strip out inline images as well as other odd formatting issues. Use TextEdit (with rich formatting off) on a Mac, or Notepad on a Windows. But the "Paste without formatting" given in my first sentence will handle almost all scenarios.
What do you cut or copy? What format is the file from which you cut or copy?
I'm not sure what formats specifically show up in tables - I'll have to watch more closely. However, they are ones I was copying from before without this issue. One source was a list of jokes from which I print out a few pages at a time for an elderly aunt, who loves them. I've been assuming that I had accidentally engaged one of Writer's features. When I copy from my docs or from emails, though, this doesn't happen. Thanks for the interest.