Copyright applies as much to Web as to print
Be especially careful of using copyright images
If in doubt, find copyright-free images
Copyright is a hazy issue on the Internet — mainly because the law has not adapted yet to cope with the new medium. Test cases regarding copyright violation are few, and are often too specific to be applied as precedents across the board.
Copyright of images is a particular problem. It's very easy to download a graphic that would suit the page you're creating and include it in your own pages. There have been many projects and proposals to include digital watermarks or copy protection into images, but none has proved practical enough to become widespread yet.
There are a number of websites that have collections of copyright-free images that can be used in your web pages. Wikipedia has a large image bank, with clear indications of copyright status. Photo-sharing sites such as Flickr allow sharers to place their images in the public domain, or release them with an open licence.