For U.S. case law regarding the display of thumbnails in image search results, see e.g. Perfect 10, Inc. v. Amazon.com, Inc. To quote from the Wikipedia article:
"The Ninth Circuit did, however, overturn the district court's decision that Google's thumbnails were infringing. Google's argument, which was upheld by the court, was a fair use defense. The appellate court ruled that Google's use of thumbnails was fair use, mainly because they were 'highly transformative.' Specifically, the court ruled that Google transformed the images from a use of entertainment and artistic expression to one of retrieving information, citing the similar case, Kelly v. Arriba Soft Corporation. The court reached this conclusion despite the fact that Perfect 10 was attempting to market thumbnail images for cell phones, with the court quipping that the 'potential harm to Perfect 10's market remains hypothetical.'"