See the links sidebar.
The list is by no means comprehensive, but rather just includes those journals I've found of good use recently and/or have web content helpful for research purposes (i.e. issue table of contents). The dominating presence of Trans-Mississippi and Western journals simply reflects my own personal research interests. The list will be updated periodically as more come to mind for inclusion.
BTW, G.E. Rule (of the great Civil War St. Louis website) has kindly searched through Missouri Historical Review and listed for us all the Civil War related articles from 1906-2002. See here.