I am guessing that most of these images were government works (e.g. government hired photographers, military photographers, etc).
Rather than guessing - why not find out for certain?
Can I publish Civil War photos on my site that were taken from, say, the University of Maryland's archives? The University says that I can not do so.
Asked and answered in the same paragraph
But, my site falls under the "Fair Use Doctrine" under U.S. copyright law that provides for the licit, non-licensed citation or incorporation of possible copyrighted material. This means that those images, according to US law, can only be used by my website for purposes such as criticism, comment, news reporting, teaching, scholarship, or research and is therefore not an infringement of copyright as this website's sole purpose is to educate and research the Civil War era.
If your web site is in fact a historical study and education site, as opposed to just a gallery - then you would potentially be correct - it would be for a legal person to make the final decision though - not you.
How can the University tell me what I can't do with these photos if they were taken by government entities during the Civil War?
If they now own the copyright to the photos - regardless of who took them originally, then they can tell you what ever they want to tell you.
What if someone had a collection of their photographs that their grandfather took during World War I and then donated them to the University. Can the University copyright these photos even though the grandfather took them for the government?
It all depends on whether the copyright was transfered as well - if it was, then the University can do with them as it wished.
But, what happens if the grandfather took these photographs for his personal use during WW1 (or WWII). Does that make it "government works" and is therefore still required to be in the Public Domain as per the copyright law?
Nope - they are personal, and he retains coptyright until he decides to transfer that to someone else, or it expires.
And, finally, lets say I have a bunch of images on my website that are not in the public domain, but falls under the "fair use" doctrine....and what if I run a bunch of popunders, adsense, etc and make a killing off the traffic? I am therefore making money...but I am not selling the photos...am I still breaking the "fair use" doctrine by making money this way?
So long as you are using them as "fair use" - then you are allowed to use them commercially - but be careful that the usage is genuine fair use for editorial, and not just padding and gallery useage. If you are using them commercially, then you are MORE likely to be sued than if you were just a missguided hobby user.