Most chess engines will let you set up board positions to start from and if you set white and black to human you can move all the pieces. If all you want is to move the pieces around you can do that with the game explorer board on this site.
Chess program
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I'm looking for a program that I can use to move chess pieces where I like and to analyze my games. Should I be using a chess engine? I mainly want to be able to move pieces anywhere, for example to recreate a position from a game, or from a lesson.
Here is a link to a lesson in which he can move any pieces around.
http://www.youtube.com/watch?v=M1qgxLYZGKA&feature=PlayList&p=DA34E99B85E50424&playnext=1&index=3