The Shapefile format is an old format which has no scope for a password or encryption. So all the solutions that you will find, will be built on top of the existing standards, and hence will not be standard across various applications. A solution that will work with ArcGIS will not work with Qgis and so on.
Having said that, I have seen a few low-tech ways of solving this problem such as:
- Windows Domain Account based folder permissions.
- Storing your files in a Trucrypt partition.
- Transporting the files in a password protected Zipped file and so on.
Having said that, I wouldn't suggest any of them. If you have data to protect, you should use standard secure ways of accessing and storing the data, like in a geodatabase (be it PostGIS or ArcSDE). Keep in mind, that once you have given someone even read only access to a geodatabase, It is easy enough for that person to export the data to another format and use it howsoever (s)he might want to use it.
The Only true secure way, is to not give even read access to the data, and only provide processed data like a WMS service or a printed map.