I am the proud direct descendant of at least two Civil War veterans: my maternal 3rd-great grandfather, George A. Holcomb from Vergennes/Panton, Vermont and my paternal 2nd-great grandfather, Edward Bailaw, from Peacham, Vermont. Edward's four brothers also fought in the Civil War, one of which died during the war and is buried in the Arlington National Cemetery. I even recently applied for membership with the Daughters of Union Veterans of the Civil War, 1861-1865 (There is also an organization of Sons of the Union Veterans of the Civil War).
Vermont has a wonderful resource for Civil War history and veterans, and is an invaluable resource for genealogists tracing their Vermont Civil War veteran ancestors. The website can be found here, and lists information including veteran names, birth dates, death dates, burial locations, and more. It also provides histories of the regiments, which is nice to read through to learn what your ancestor may have gone through during the war.
Other Vermont Civil War resources are included in the following list:
1) Wikipedia information about Vermont in the American Civil War: While I do not believe that Wikipedia should be the one-stop source of information for anything, it is a good starting point. Just keep in mind that anyone is free to create and edit Wikipedia pages, so take what you learn here with a grain of salt.
2) Rootsweb Vermont in the Civil War Discussion List: This is a mailing list for people to discuss Vermont in the Civil War.
3) Vermont Veterans Militia Museum: Civil War
4) A War of the People: Vermont Civil War Letters: Book
5) The Vermont Fist Calvary in the Civil War: Book