Can civilians buy military aircraft?
You could, if the aircraft is available for sale somewhere, and there are no other legal compliance problems. Paul Allen has a nice collection of military aircraft at his Flying Heritage Collection, and there are certainly quite a few other people with both flyable and unflyable military aircraft. There are also private companies which will let you try out their planes, such as Australian Jet Adventures

Here is a web site which tracks military planes in private ownership around the world:

http://www.warbirdalley.com/