You can use the images if you have the consent of the copyright owner of the images, if you are the copyright owner of the images, or if the image is labelled for reuse. Doing otherwise can result in unwanted penalties that could have been easily avoided.
For example, in the case that you were to visit one of my websites, pilfer my images, and then place them on your website (with or without a source is irrelevant), this would leave you vulnerable to immediate litigation as I am not required to give you a warning before becoming litigious. These penalties are not low, either; they can range
as low as $200 to as high as $150,000.
However, most copyright owners will either not care or they will ask for a link back to their website in exchange for using their images, although there have been cases where
the copyright owner of an image has decided to sue the infringer without any prior warning. Again, this doesn't happen often, but I personally do not take the risk and only use images that I've created or images that have been labelled for reuse.