1. when ever you are doing validations in your test you need to fetch data from the Object's in varying fashion as per your requirement...for eg:if your requirement to test the IE Window for some application that has title bar appended by the Account ID that is unique for an Individual, for testing that you need to parse the text of the title there comes SCRIPTING.

2. In specific case when-ever there are custom controls that are not identified uniquely by QTP we need to write Functions that do parsing of the Data and provide the requirement.

3. In Case there are some keyboard enabled events in your test, you are required to perform shell programming to trigger those event(shell scripts).

4. VBScript functions are used to filter the data that appears in the application for test purpose.

5. Regular Expressions are used to setup some parameterize checkpoints that are in case not Feasible with the QTP inbuilt Checkpoints.

6. In case you want to interact with the OTA of QTP or some integrated tools API's are processed and supported by VBScript..

Lot's more to be added...Thank's for starting this thread..hope there will be more addition's to the above list.

Regards,
Nawab