Alexander Street Press is offering free access to their online Civil War collection for all of June. It includes a comprehensive index of 4.3 million soldiers and thousands of battles, as well as databases for letters and diaries, newspapers and magazines, and photographs, posters, and ephemera.
As always, several government agencies, most notably the Library of Congress, have online Civil War archives that are always free.

The American Civil War Online [Alexander Street Press]
US Civil War: Selected Resources including Photographs and Maps [Library of Congress]
Civil War, forging a more perfect union [National Park Service]

"Antietam, Md. Battlefield on the day of the battle" from the Library of Congress' Selected Civil War Photographs collection