Text content on a web page is subject to copyright; use or redistribution requires permission of the copyright holder (author, publisher, etc.)
Just because it is posted on the web (and therefore easy to copy) doesn't mean it is in the public domain! Always look for copyright symbols or notices. Many sites explicitly state that their material and graphics are copyrighted.
Many sites will state that their images are freely downloadable, or downloadable with restrictions. If in doubt about the legality of using an image downloaded from a site, DON'T!
Just because it's old doesn't mean it is in the public domain: for example, an image of the Mona Lisa is still copyrighted by the Louvre.
A special word of caution about cartoons: syndications are actively pursuing litigation against anyone who is using copies of their cartoons in a Web document, so DON'T put a Calvin and Hobbes strip on your home page! The same goes for logos.