Archivists' Toolkit and ArchivesSpace are two free, open-source computer applications for archival collections management.
Archivists' Toolkit was one of the most commonly used programs for archival collection management until it was superceded in late 2013 by ArchivesSpace. Archivists' Toolkit offers some features that are not available in ArchivesSpace, such as an assessments module and the ability to export PDF versions of finding aids, so many professional archives are continuing to use it in 2015. It is still available for download. Ideally, a separate database program such as MySQL should be used in tandem with Archivists' Toolkit; if the program will only be used on one computer, however, the internal built-in database should suffice. (Instructions for downloading the internal database are here.) Because Archivists' Toolkit has been used successfully by archives for several years, there are many freely available resources and manuals online, such as this one from the Philadelphia Area Consortium of Special Collections Libraries (PACSCL).
ArchivesSpace is free to download and run, although one must become a paying member for access to user support and documentation. However, because it is recently released, there are not as many online manuals and resources for it.