Unfortunately, I lot of them have been knocked down and replaced by more modern structures.
Those I don't even bother photographing.
But when I see a nice courthouse dome or spire peaking above the trees in a town, I just have to make a detour and take a photo.
On our trip from Seattle to Minneapolis via US-12 we came across a couple of nice courthouses.
This is the Brown County, South Dakota courthouse in Aberdeen, SD. Built in 1904, it is a Renaissance Revival style building. I absolutely love that there are clocks on all four sides of the dome structure. I think the statue atop the dome is Justice, but am not positive. Forgot to bring my binoculars along!
At right is the Swift County, Minnesota courthouse in Benson, MN. It was built in 1898 to replace an earlier courthouse that proved too small to meet the growing county's needs. There are some old postcard images of this courthouse here.
Pity all county seats don't have such classic courthouses, isn't it?