In ArcGIS 10.1, wherever you are prompted to select a coordinate system (data frame properties for instance), you can right click and save a highlighted coordinate system to your machine. The closest way to achieve what you're looking for is the save all of the projection files you regularly use to a shared folder or network drive, and for each individual user, import the saved prj files as new coordinate systems (using the Import option in the coordinate system window). This will place them in the Favorites folder. As you noted, ArcGIS 10.1 also has a 'Favorites' feature detailed below, which if you are working on the same machine/same user every time would be the easiest approach.
See here for more info.
ArcGIS for Desktop 10.1 supports over 5,000 geographic, projected and
vertical coordinate systems. Before ArcGIS 10.1, coordinate systems
were included in the installation directory as .prj files in a
Coordinate Systems folder. Installing the .prj files required a
significant portion of the time taken up by the software installation
To improve the installation experience and simplify localization
support, the files are no longer included in the installation package.
Instead, a virtual directory structure is built directly from the
coordinate system data.
Commonly used coordinate systems can be exported to a Favorites
folder. The Favorites folder is stored in the user profile location,
which depends on the computer operating system used. The Favorites
directory can be accessed in ArcMap when setting the coordinate system
of an ArcMap data frame on the View > Data Frame Properties menu,
Coordinate System tab.
The coordinate systems in the Favorites directory are also available
in ArcToolbox when using the Define Projection tool or the Project