This one comes up from time to time. Here's what I remember :
The solution we probably all want (mark them as "archived" so they
automatically disappear from most views but can be brought back when needed)
doesn't seem to exist. The two most common solutions seem to be :
1. Save the project as a .mpp file and delete from Project Server.
2. Define an Enterprise Outline Code (or any Enterprise custom field, I
guess) to indicate an Archived project, set it to a different value for
completed projects, and either edit your standard views or (better) create
new views in PWA which will only show projects that do not have this flag
set.
I don't think we ever found a solution for hiding completed projects from
the Open dialog in Project Professional, although if you train your PMs to
always open projects using the Open button in PWA (using a view that omits
completed projects) that is probably close enough.
JB