All you need to do is append the new string to the existing list
% prompt the user for some input
answer = inputdlg(prompt,name,numlines,defaultanswer,'on');
% get the current list box selections
selections = get(handles.componentlistbox,'String');
% append the answer to the list
selections = [selections ; answer];
% update the list box with the new selection
set(handles.componentlistbox,'String',selections);
Note that in the above, the answer is not being saved to handles.answer as that duplicates what is in the list box.
Note also that you should put in a check of some kind to ensure that duplicate entries aren't added to the list.
Try the above and see what happens!
