Allow "Add New" on drop-down field?

[simplescience]

Has anyone successfully created a drop-down field and changed the code to allow for an "Add New" option to that same drop-down (option list)?

We would like for a user to either select from a drop-down list, or add their own value to that field and option list.

Thanks to all in advance for any help.

[DSIN]

I am also looking for the same feature, I wonder if it can be done with a module. I have a Dropdown which is populated by an internal form but if the company is not in the list I want to provide the user a way to add the company without giving them admin access to the Forms backend.