> Can you actually copy someone else's images and serve them from your own website

Short answer: No

Long answer: It depends. On your personal site that has ads, a donate button, or products/services you sell: highly unlikely. See links below.

* http://en.wikipedia.org/wiki/Fair_use#Fair_use_under_United_...

* http://en.wikipedia.org/wiki/Copyright_law_of_the_United_Sta...

This is not legal advice. IANAL, etc.