This is not a question about the differences between I understand that a Hashtable and HashMap.Hashtable object cannot accept
Knowing when to use one class or structure over another is essentially understanding the differences between the two, and deciding which one best suits the problem at hand based on those differences.
I understand that a Hashtable object cannot accept null values
So in the situation where you need to store null values, a Hashtable would not be appropriate.
Also, in a Hashtable, enumeration is not fail-safe. So if you need to be able to change the content of the structure while enumerating, a Hashtable would be more appropriate.