A Queue that ensure uniqueness of the elements?

How about a LinkedHashSet? Its iterator preserves insertion order, but because it's a Set, its elements are unique.

As its documentation says,

Note that insertion order is not affected if an element is re-inserted into the set.

In order to efficiently remove elements from the head of this "queue", go through its iterator:

Iterator<?> i = queue.iterator();
...
Object next = i.next();
i.remove();

This doesn't exist as far as I know but would be fairly simple to implement using a LinkedList in conjunction with a Set:

/**
 * Thread unsafe implementation of UniqueQueue.
 */
public class UniqueQueue<T> implements Queue<T> {
  private final Queue<T> queue = new LinkedList<T>();
  private final Set<T> set = new HashSet<T>();

  public boolean add(T t) {
    // Only add element to queue if the set does not contain the specified element.
    if (set.add(t)) {
      queue.add(t);
    }

    return true; // Must always return true as per API def.
  }

  public T remove() throws NoSuchElementException {
    T ret = queue.remove();
    set.remove(ret);
    return ret;
  }

  // TODO: Implement other Queue methods.
}

I'd be tempted to maintain a HashSet containing a key that uniquely identifies the items in the queue side-by-side with it. Then just check the HashSet to see if the item is in the queue before adding it. When you remove an item from the Queue, simply remove the key from the HashSet as well.

Just to complete Adamski's answer:

/**
 * A queue that keeps each element only once. 
 * If you try to add an element that already exists - nothing will happen.
 * 
 * @author Adamski http://stackoverflow.com/a/2319156/827927
 * @NotThreadSafe
 */
public class UniqueQueue<T> implements Queue<T> {

private final Queue<T> queue = new LinkedList<T>();
private final Set<T> set = new HashSet<T>();

@Override public boolean add(T t) {
    // Only add element to queue if the set does not contain the specified element.
    if (set.add(t))
        queue.add(t);
    return true; // Must always return true as per API def.
}

@Override public boolean addAll(Collection<? extends T> arg0) {
    boolean ret = false;
    for (T t: arg0)
        if (set.add(t)) {
            queue.add(t);
            ret = true;
        }
    return ret;
}

@Override public T remove() throws NoSuchElementException {
    T ret = queue.remove();
    set.remove(ret);
    return ret;
}

@Override public boolean remove(Object arg0) {
    boolean ret = queue.remove(arg0);
    set.remove(arg0);
    return ret;
}

@Override public boolean removeAll(Collection<?> arg0) {
    boolean ret = queue.removeAll(arg0);
    set.removeAll(arg0);
    return ret;
}

@Override public void clear() {
    set.clear();
    queue.clear();
}

@Override public boolean contains(Object arg0) {
    return set.contains(arg0);
}

@Override public boolean containsAll(Collection<?> arg0) {
    return set.containsAll(arg0);
}

@Override public boolean isEmpty() {
    return set.isEmpty();
}

@Override public Iterator<T> iterator() {
    return queue.iterator();
}

@Override public boolean retainAll(Collection<?> arg0) {
    throw new UnsupportedOperationException();
}

@Override public int size() {
    return queue.size();
}

@Override public Object[] toArray() {
    return queue.toArray();
}

@Override public <T> T[] toArray(T[] arg0) {
    return queue.toArray(arg0);
}

@Override public T element() {
    return queue.element();
}

@Override public boolean offer(T e) {
    return queue.offer(e);
}

@Override public T peek() {
    return queue.peek();
}

@Override public T poll() {
    return queue.poll();
}
}