Although it was not always the case, Flickr currently allows users to set the copyright restrictions (licensing) for uploaded photos. While many Flickr photos can be used without fee, many others cannot. To protect yourself from accidentally illegally copying a photo you need to know where the copyright data can be found on Flickr.
To find copyright data look in the far right bottom corner of the photo screen in Flickr. There is a small area under "Owner Settings" that lists the copyright/licensing status. In the example photo this is set to "© All Rights Reserved." This means that the photo can not be copied or used in any way without my permission.