MenuPreference.java

public class MenuPreference extends ListPreference {
  private View anchor;

  public MenuPreference(Context context) {
    super(context);
  }

  public MenuPreference(Context context, AttributeSet attrs) {
    super(context, attrs);
  }

  @Override
  protected View onCreateView(ViewGroup parent) {
    return anchor = super.onCreateView(parent);
  }

  @Override
  protected void showDialog(Bundle state) {
    final PopupMenu popup = new PopupMenu(getContext(), anchor, Gravity.TOP);
    final Menu menu = popup.getMenu();
    
    for (int i = 0; i < getEntries().length; i++) {
      MenuItem item = menu.add(1, i, Menu.NONE, getEntries()[i]);
      item.setChecked(item.getTitle().equals(getEntry())); // 1
    }
    menu.setGroupCheckable(1, true, true); // 2

    popup.setOnMenuItemClickListener(new PopupMenu.OnMenuItemClickListener() {
      @Override
      public boolean onMenuItemClick(MenuItem item) {
        popup.dismiss();
        String value = getEntryValues()[item.getItemId()].toString();
        if (callChangeListener(value))
          setValue(value);
        return true;
      }
    });
    popup.show();
  }

}

Adding a comment from the original gist:

A MenuPreference showing a menu instead of an old ListPreference (a modal simple dialog), as recommended by http://www.google.com/design/spec/components/menus.html#menus-simple-menus.

Items 1 and 2 (see comments) are optional if you want to have radio buttons. Checkboxes can be specified similarly.