I see this question often and have answered it back when people were moving off of QC10:
Basically, you could re-arrange the Project-''tree'' structure in Site Admin so you have an additional ''archive'' domain, then move/migrate or upgrade projects into the new ''Archive'' domain, then upgrade them (if in the midst of an upgrade) and confirm that they work. then, you can DEACTIVATE them to save on server performance (less CPU cycles used for QC to monitor unused projects). They can be quickly re-activated as needed.
If the projects are really archival bound (most likely not needed unless there is an Audit or something), you could EXPORT the projects to QCP (self-contained project dump files).
These QCPs can be re-imported as needed, BUT BEWARE that they are VERSION-specific and if you later upgrade your server, they cannot be imported to a newer server (see my earlier post related to archival from QC10 link above).
more about QCP files in this post:
Archival via QCP files also frees up DB and repository space as the projects can be deleted from the server.
!!!! Make sure you have a GOOD BACKUP of ALL QC project DB's and Repository before doing this kind of ''cleanup''. It may also be a good idea to test the QCP file integrity for ability to import to a DIFFERENT/Test server of the same version as the source server the QCP was created from.