YES!  Copyright is VERY important.  Images fall under the category of INTELLECTUAL PROPERTY, they are the property of the creator no matter where you might find them (in a book, on the web, in a magazine, etc.)

Be sure the creator is willing to share their intellectual property with you before you incorporate an image into your work.

To learn more about the protections of copyright, have a look at this video (4 mins 40 secs).

People who WANT to have their work reused can post their work with as Creative Commons (CC).  Creative Commons is a set of licenses that enables others to freely and lawfully copy, post  and reuse original work. 

To learn more about opportunities to to use works shared with Creative Commons licenses, have a look at this video.