Take a look at the Doc.mailForm() method (see here for the documentation: http://help.adobe.com/livedocs/acrobat_sdk/11/Acrobat11_HTMLHelp/wwhelp/wwhimpl/common/html/wwhelp.htm?context=Acrobat11_HTMLHelp&file=JS_API_AcroJS.89.512.html)
The first thing you should do is add the email address as export values to your dropdown control: When you bring up the field properties and go to the "Options" tab, you can specify display value (which will be displayed on the control), and an export value, which will be used when you get the selected value.
You can then add a "Submit" button to your document with a Javascript action that first gets the email address from the dropdown control (because we are using the email address as export value, that's what we are getting), and then call the mailForm() method to submit the document:
var email = this.getField("Dropdown").value;
this.mailForm(false, email);
You can add more information (e.g. a subject or a body for the mail message), all that is explained in the documentation.
Karl Heinz Kremer
PDF Acrobatics Without a Net
PDF Software Development, Training and More...
http://www.khkonsulting.com