Scott is partially correct. All images are, by default, copyrighted in the United States, unless...
- otherwise noted, or...
- the copyright has expired
There are many additional exceptions as well. Lese mentioned one:
Creative Commons licensing. One can also put something in the public domain, or open source it.
Copyrights also expire, though the media industry in the US is constantly trying to stop that. For instance, the Mona Lisa is not copyrighted. Where it gets confusing is that a photo of the Mona Lisa is copyrighted--even if the subject matter isn't.
As for what you can use, whether you or your client is a for-profit vs. non-profit entity is irrelevant. If it's commercial work, you need to clear copyrights to be within the law.
Again, though, there are exceptions. Fair use being the big one. What constitutes fair use, however, is also under fire from the media industries, so that's a crapshoot as well.
Sadly, copyright law can be a murky mess of rules and lawsuits.
NOTE: that the above pertains to US Intellectual Property law. It's a big planet with lots of laws so things may very well vary greatly in your neck of the woods.