The pension files may contains a variety of information which could include depositions regarding military service, letters and certificates. The pension file for one of my ancestors contains his parole pass from Appomattox.
The states which issued Confederate pensions are Alabama, Arkansas, Florida, Georgia, Kentucky, Louisiana, Mississippi, Missouri, North Carolina, Oklahoma, South Carolina, Tennessee, Texas and Virginia.
There are published indexes for some of the state's pension files and for some there is microfilm. The originals are in repositories such as the state archives or state library. Copies from microfilm or the originals can usually be obtained for a fee. Some of the pension files have been digitized. Be sure to also check the Family History Library Catalog (LDS) for available microfilm.
Alabama - Alabama Department of Archives and History http://tinyurl.com/5wd5va8
Arkansas - Arkansas History Commission
two online indexes at http://tinyurl.com/69vjw34
Florida - State Library and Archives of Florida
digitized images in PDF at http://www.floridamemory.com/collections/pensionfiles/
Georgia - Georgia Archives/Georgia Virtual Vault
scanned images at http://cdm.sos.state.ga.us/cdm4/pension.php
Kentucky - Kentucky Department of Libraries and Archives
indexes have been published
order form for copies of records at http://www.kdla.ky.gov/research/military.htm
Louisiana - Louisiana State Archives, Genealogy and History Section
index online at http://www400.sos.louisiana.gov/archives/gen/cpa-alpha.htm
Mississippi - Mississippi Department of Archives and History
microfilmed
information at http://mdah.state.ms.us/arrec/refreq.php
Missouri - The Missouri State Archives
guide to resources - http://www.sos.mo.gov/archives/resources/civilwar/intro.asp
North Carolina - North Carolina Division of Archives and History
microfilmed
index at North Carolina State Archives (select MARS Catalog tab)
Oklahoma (Indian Territory)
index at http://www.odl.state.ok.us/oar/docs/pension.pdf
information at http://www.okhistory.org/research/library/military.html
South Carolina - South Carolina Department of Archives and History
information at http://tinyurl.com/66lfh52
search form at http://www.archivesindex.sc.gov/onlinearchives/search.aspx
(record group should be Records of Confederate Veterans, 1909-1973)
Tennessee - The Tennessee State Library and Archives
index - Tennessee Confederate Pension Applications: Soldiers and Widows
order by mail - http://www.tennessee.gov/tsla/history/mailmil.htm
Texas - The Texas State Library and Archives Commission
searchable index - Confederate Pension Records
Virginia - Library of Virginia/Archives Division
guide - http://www.lva.virginia.gov/public/guides/Civil-War/
search - http://tinyurl.com/65mjkjd (links to images)
Keep in mind that Confederate veterans who were living in the western or southwestern areas of the United States after the Civil War, may have applied through the state where they had served.