As explained earlier, using someone else's copyrighted work is not permitted without a license. If the work does not indicate that it is copyrighted, it does not mean there is no copyright, it only means you will have to contact the author to find out what you may do with it. Most Websites these days have explicit licenses, which list in detail what is and what is not permitted.
Pay particular attention to sites that offer collections of images, sounds and the likes. Most "icon archives" have a large number of icons from various sources, and offer these under their own license. However, each individual icon is copyrighted by its creator, and unless this person has given the icon archive a license, the archive is not permitted to make that icon available. So do not immediately trust that an icon you find on a public archive can be used freely.
More information on patents, copyright, trademarks and other Internet-related law is available on Iusmentis.com.