Platform: all
JDK: 1.1+
Class. java.awt.Toolkit
Methods:
example - http://download.java.net/jdk7/docs/api/java/awt/Toolkit.html#loadSystemColors%28int[]%29
and the same with:
          http://download.java.net/jdk7/docs/api/java/awt/Toolkit.html#setDynamicLayout%28boolean%29
          http://download.java.net/jdk7/docs/api/java/awt/Toolkit.html#getMenuShortcutKeyMask%28%29
          http://download.java.net/jdk7/docs/api/java/awt/Toolkit.html#getLockingKeyState%28int%29
          http://download.java.net/jdk7/docs/api/java/awt/Toolkit.html#setLockingKeyState%28int,%20boolean%29
          


    ------------
    protected void loadSystemColors(int[] systemColors) throws HeadlessException
    Throws:
        HeadlessException - if GraphicsEnvironment.isHeadless() returns true
    ------------

In fact, default version of this method doesn't throw HE in HeadlessEnvironment

Please see, compile and execute with "-Djava.awt.headless=true" the following code sample:
HeadlessException won't be thrown

-----------------------------------------------------
import java.awt.*;
import java.awt.datatransfer.Clipboard;
import java.awt.dnd.*;
import java.awt.dnd.peer.DragSourceContextPeer;
import java.awt.font.TextAttribute;
import java.awt.im.InputMethodHighlight;
import java.awt.image.*;
import java.awt.peer.*;
import java.net.URL;
import java.util.Map;
import java.util.Properties;

public class NoHE {

    public static void main(String[] args)  {
         new _Toolkit().loadSystemColors(new int[10]);
    }

    static class _Toolkit extends Toolkit {

        @Override
        public void loadSystemColors(int[] systemColors) throws HeadlessException {
            super.loadSystemColors(systemColors);
        }

        @Override
        protected DesktopPeer createDesktopPeer(Desktop target) throws HeadlessException {
            return null;
        }

        @Override
        protected ButtonPeer createButton(Button target) throws HeadlessException {
            return null;
        }

        @Override
        protected TextFieldPeer createTextField(TextField target) throws HeadlessException {
            return null;
        }

        @Override
        protected LabelPeer createLabel(Label target) throws HeadlessException {
            return null;
        }

        @Override
        protected ListPeer createList(List target) throws HeadlessException {
            return null;
        }

        @Override
        protected CheckboxPeer createCheckbox(Checkbox target) throws HeadlessException {
            return null;
        }

        @Override
        protected ScrollbarPeer createScrollbar(Scrollbar target) throws HeadlessException {
            return null;
        }

        @Override
        protected ScrollPanePeer createScrollPane(ScrollPane target) throws HeadlessException {
            return null;
        }

        @Override
        protected TextAreaPeer createTextArea(TextArea target) throws HeadlessException {
            return null;
        }

        @Override
        protected ChoicePeer createChoice(Choice target) throws HeadlessException {
            return null;
        }

        @Override
        protected FramePeer createFrame(Frame target) throws HeadlessException {
            return null;
        }

        @Override
        protected CanvasPeer createCanvas(Canvas target) {
            return null;
        }

        @Override
        protected PanelPeer createPanel(Panel target) {
            return null;
        }

        @Override
        protected WindowPeer createWindow(Window target) throws HeadlessException {
            return null;
        }

        @Override
        protected DialogPeer createDialog(Dialog target) throws HeadlessException {
            return null;
        }

        @Override
        protected MenuBarPeer createMenuBar(MenuBar target) throws HeadlessException {
            return null;
        }

        @Override
        protected MenuPeer createMenu(Menu target) throws HeadlessException {
            return null;
        }

        @Override
        protected PopupMenuPeer createPopupMenu(PopupMenu target) throws HeadlessException {
            return null;
        }

        @Override
        protected MenuItemPeer createMenuItem(MenuItem target) throws HeadlessException {
            return null;
        }

        @Override
        protected FileDialogPeer createFileDialog(FileDialog target) throws HeadlessException {
            return null;
        }

        @Override
        protected CheckboxMenuItemPeer createCheckboxMenuItem(CheckboxMenuItem target) throws HeadlessException {
            return null;
        }

        @Override
        protected FontPeer getFontPeer(String name, int style) {
            return null;
        }

        @Override
        public Dimension getScreenSize() throws HeadlessException {
            return null;
        }

        @Override
        public int getScreenResolution() throws HeadlessException {
            return 0;
        }

        @Override
        public ColorModel getColorModel() throws HeadlessException {
            return null;
        }

        @Override
        public String[] getFontList() {
            return new String[0];
        }

        @Override
        public FontMetrics getFontMetrics(Font font) {
            return null;
        }

        @Override
        public void sync() {

        }

        @Override
        public Image getImage(String filename) {
            return null;
        }

        @Override
        public Image getImage(URL url) {
            return null;
        }

        @Override
        public Image createImage(String filename) {
            return null;
        }

        @Override
        public Image createImage(URL url) {
            return null;
        }

        @Override
        public boolean prepareImage(Image image, int width, int height, ImageObserver observer) {
            return false;
        }

        @Override
        public int checkImage(Image image, int width, int height, ImageObserver observer) {
            return 0;
        }

        @Override
        public Image createImage(ImageProducer producer) {
            return null;
        }

        @Override
        public Image createImage(byte[] imagedata, int imageoffset, int imagelength) {
            return null;
        }

        @Override
        public PrintJob getPrintJob(Frame frame, String jobtitle, Properties props) {
            return null;
        }

        @Override
        public void beep() {

        }

        @Override
        public Clipboard getSystemClipboard() throws HeadlessException {
            return null;
        }

        @Override
        protected EventQueue getSystemEventQueueImpl() {
            return null;
        }

        @Override
        public DragSourceContextPeer createDragSourceContextPeer(DragGestureEvent dge) throws InvalidDnDOperationException {
            return null;
        }

        @Override
        public boolean isModalityTypeSupported(Dialog.ModalityType modalityType) {
            return false;
        }

        @Override
        public boolean isModalExclusionTypeSupported(Dialog.ModalExclusionType modalExclusionType) {
            return false;
        }

        @Override
        public Map<TextAttribute, ?> mapInputMethodHighlight(InputMethodHighlight highlight) throws HeadlessException {
            return null;
        }
    }
}

-----------------------------------------------------
The following methods are still not fixed in JDK7 b140

          http://download.java.net/jdk7/docs/api/java/awt/Toolkit.html#getLockingKeyState%28int%29
          http://download.java.net/jdk7/docs/api/java/awt/Toolkit.html#setLockingKeyState%28int,%20boolean%29

The following tests still fail

api/java_awt/Toolkit/indexTGF.html#HeadlessExceptions[setLockingKeyState_defaultMethodImpl]
api/java_awt/Toolkit/indexTGF.html#HeadlessExceptions[getLockingKeyState_defaultMethodImpl]