Remember that you do not need permission if you are using something that is not copyrightable or is in the public domain. You also don't need permission if you are using it in a way that does not implicate one of the rights of copyright holders or is permitted by a user’s right, such as fair use. For more information on these topics, please consult Copyright Basics.
Because images are so often published without attribution, it can be especially difficult to locate their copyright holders. If you have an image you would like to license but need to identify and contact the copyright holder, a reverse image search engine may be helpful. You can use a reverse image search engine to find out where an image came from, where it is being used, and whether higher resolution or modified versions of the image exist.
The sites below offer images that are licensed for reuse or are in the public domain. The Images research guide provides a more comprehensive list of such sites.
Some of these images are "free" -- for others there is a fee. "Royalty-free" means that you don't have to pay royalty fees for use, but you may still have to pay a fee for the image. Visit these sites with caution as the pop-up ads can be invasive and read the fine print before you use any image.
For a recent (Dec 2017) overview of 85 stock photo and license free image sites, with an emphasis on Creative Commons and Public Domain images, see this article by Jake Rheude: 85 Free Stock Photo Resources -- How to Use Them.