Favorite module allows to add property to "My favorite" list
You can access your My Favorite e.g. via top bar:
This option is the most useful when you allow public registration.
When not logged in user will click favorite it will ask to register/login on your website (you can choose in your panel which tab is active at start):
It is not possible to use Favorite module with not registered users. For not registered users we recommend compare - Compare Properties module - how it works?