Here's a link to one of my favorite articles about counterstamps:
http://earlyusquarters.com/ARTICLES...icalpast.pdfAdvertising goods and services was the principal reason for counterstamping coins. The above article illustrates and discusses a handful of those truly classic counterstamps. You'll note that the article describes some political and government generated counterstamps, too.
There were a good many other reasons that coins were counterstamped, and I've not as yet seen a comprehensive listing of all plausible reasons, yet Brunk and Rulau cite a good many in their work. Here are some reasons that collecting experience has brought to my mind:
- To serve as an ID of a maker's mark (gunsmith - such as my avatar, silversmith, etc.)
- To serve as a check (hat check, return of repaired item like a watch, etc.)
- To serve as a counter (card game like whist, etc.}
- To serve as a personal ID (Masonic Penny, other, etc.)
- To gain admission (Pay at the door, receive c/s)
- As a prize or gift (Used as promotion for a show)
- To test newly made punches
- As tool checks for workmen to assure return of borrowed tool
- As a memento (personal, political, historic ... e.g. - McKinley's Funeral Train)
- To illustrate a patent mark on a product, invention
- To illustrate a relationship between two or more individuals (working, fraternal, etc.}
- To indicate a work tally, serve as a product counter (bucket, tray filled, number produced, etc.)
- To test for metal's purity, plating (chopmarks ...)
- To indicate a business successor (c/s on token)
- Use as a security device (to ID stolen property)
- To alter denomination or worth (national or private)
- To serve as a transportation or travel token
- Whimsy ...

Well, this is about all that I can come up with right now. Perhaps, some others may chime in? Thanks for asking that excellent question!