Adobe always prints with colored and black/white squares on top

I know this thread is almost 3 years old, but just a heads up in case anyone runs into this issue (like I did) - there's a chance this will work for you as well.

Had a user ask me how to remove the color marks when printing. I checked the advanced printing options and confirmed that all marks were disabled, and even tried toggling them on and off multiple times in case the setting got stuck or didn't apply properly, but no luck - they were still there. 

I was about to give up and tell the user she would need to contact the creator and ask them to send her a version with the color marks disabled, but as a last-ditch effort I checked the layers of the document and saw that one was called "Marks & Bleeds". I disabled that layer, showed the user, and she said that was exactly what she needed!

So that worked for us! If anyone comes here with the same issue, might be worthwhile to check and see if your document has layers (in my experience, not all PDFs do); if so, you may be able to disable the "Marks & Bleeds" layer to get rid of the color marks. 

Do you see them only when you print the document?

If so, you've somehow inadvertently turned on Printer's Marks under the Advanced tab in the Print dialog. These settings are sticky, so if you did it once before, it will stay that way there until you turn it off, or reselect Acrobat Default at the top of this dialog.

Do they look like these? (attached image), if so, they're color bars added when the pdf was created. They may exist on your pdf, even if you don't see them on your screen, i.e, the pdf may be cropped, which will hide (but not remove) the area beyond the crop. You can turn off the color bar option when creating your pdf.

Your printer might also have an option (under the advanced settings) to add color bars.