Better tagging / taxonomy reference widget
Select (or other) module looks like provide similar UI.


  Provides a new Forms API element which is a select/radios/checkboxes
  element that has an 'other' option. When 'other' is selected a
  textfield appears for the user to provide a custom value.


Unfortunately it doesn't support Term References.

Try Autocomplete Deluxe module or Chosen module for better UI and functionality.