In the United States and it territories, 17 U.S.C. §106 provides a copyright owner with, inter alia, the exclusive right to (1) reproduce the copyrighted work; (2) prepare derivative works of the copyrighted work; (3) distribute copies of the copyrighted work; and (4) display the copyrighted work. 17 U.S.C. §501, which provides for a copyright infringement action, does not contain a "scienter" requirement, i.e. the statute does not say that the infringer must take the action knowingly, negligently or recklessly. In other words, if you do the deed, you suffer the penalty, regardless of whether you knew you did something wrong.
Federal copyright protection attaches the moment a person reduces an expression to a form (e.g. a drawing). However, under 17 U.S.C. §412, an owner cannot sue an infringer for money damages or attorney's fees unless the copyrighted work is registered and deposited with the Patent and Trademark Office within three months after the work's creation. When an owner does not register the copyrighted work and deposit a copy at the USPTO, the owner is generally limited to injunctive relief, i.e. a court order that says the infringer cannot infringe anymore.
Sections 107 through 120 provide some exemptions from liability, including "fair use" in scholastic work, research and teaching. In effect, if you reproduce a copyrighted work for criticism, comment, news reporting, teaching, scholarship or research, such a use is not a violation of copyright.
However, there is no "I found it on the Internet" exemption. The authoritative statements that "I found it on the Internet, so it's O.K. to use" I have seen on countless boards have no basis in law. It is an Internet myth perpetuated by the legally naive.
Now, if the owner has intentionally abandoned the copyright and has knowingly placed the formerly copyrighted work into the public domain, then it's fair game. I have seen several articles on the Internet where the author has explicitly stated that he or she is placing the article into the public domain.
There is a concept called "innocent infringement" which reduces statutory damages in cases where the infringer was not aware and had no reason to believe that his or her acts constituted an infringement of copyright. It does not absolve a person of liability. In most cases, though, this doctrine has been applied to newspaper publishers, broadcasters, librarians, teachers and non-profit organizations who have infringed a copyright in an occasional or isolated use of a copyrighted work.
So the brief answer to your question is yes, you would be infringing the copyright by using an image you know to be copyrighted. Are you likely to get sued? Probably not. The owner has to catch you, and then the owner has to be concerned enough about your use to do something about it.
Unfortunately, the Internet has presented a substantial challenge to policing intellectual property rights (trademark, copyright and patent). After all, a copyright owner would have to peruse countless pages to ensure that his or her work does not appear thereupon. The law is still evolving to catch up with technology, although there has been substantial legislative action to try to keep pace.
Regards,