I'm a master student in psychology. A year ago, I downloaded a lot of free clipart online to create my study stimuli. For example, some clipart are from this website: http://clipart-library.com. I basically created my study stimuli using clipart from multiple sources. I finished writing up my thesis and plan to publish it soon. However, it occurs to me that if I publish my study with a few figures of experimental stimuli, it may incur copy right issues. I'm wondering what would be the best option for me at this moment? Should I not include any figures in my publications?
In any case, be sparing in using clip-art in a thesis.
All images on our site are for Non-Commercial Use.
So, as long your thesis has no commercial implications, you should be fine. You may want to add somewhere a reference to the website or to the individual images, like:
Adapted from 
(image source )
where  is a permanent link to the image in the repository.
Carefully distinguish between "using" an image, and republishing it. If you analyze tens of thousands of images but don't republish any of them then you are fine as long as you obtained them legally.
Copyright doesn't apply to "using" something. It applies to republishing it.
Another issue would be in play if you went around paywalls to get access. Now you are in the area of theft, not copyright.
But you can look at anything and you can think about anything and generally speaking you can write about anything. Just don't steal it and just don't republish it without permission of some kind.
As an example, if, in those tens of thousands of images you find 600 that depict Minnie Mouse, you can say so without violating any of Disney's copyrights. You can even say that in 300 of those she was dressed in red and in 200, in blue. Not a problem. Just don't include any of the images without permission.
For purposes of your thesis, just include images that you are sure are free to use for the purpose as stated by the copyright holder. As others have stated "Non Commercial" should be fine, but "Personal Use Only" maybe not.