Shapefiles, personal geodatabases, and feature classes have a default size limitation. It would be nice to view the file size in ArcCatalog to 1). Keep track of how large individual files are 2). If server space is limited, it will help in data management 3). Users can comprehend file size more easily than number of features.
At this point exporting to a third party i.e. txt, ascii, excel, etc is the only way to know the file size of the features.
Also knowing when the file was last modified would be a useful piece of information. Currently only mxd files have this information. But if the file was modified outside the mxd there is no record of what date/time. This can help deter any questions about when data is created and/or modified.
A screen showing information similar to that of a normal folder: File, File type, Data Created/Modified, Size, Author.