A dropdown is usually a list of static options the user can choose from. In some cases, however, you want to have a option like "Other" where they can enter free text.
In many forms this is accomplished by showing an appropriate row with JavaScript in case the list is a checkbox list or a radio button list.
You can have similar functionality in a RadDropDownList by creating a template that will have a textbox and to use the client-side events of the textbox to transfer its text to the Value of the dropdownlist item.
An example is attached below.
