The courts have determined that it is within fair use to download thumbnail images from a website without asking permission or paying a licensing fee.
However, downloading full size images from a web site does not meet the fair use criteria. Unless the site clearly states that it is permissible to download images for free, you must request permission and possibly pay a licensing fee to do so.
Fair Use Factors
The use of an image must meet the following criteria in order to be considered "fair use":
The purpose and character of the use, including whether such use is of a commercial nature or is for nonprofit educational purposes.
The nature of the copyrighted work.
The amount and substantiality of the portion used in relation to the copyrighted work as a whole.
The effect of the use upon the potential market for, or value of, the copyrighted work.