LinkedList.indexOf could take advantage of the fact that "header" entry has a null element for increased performance when it is passed a null "target":

    public int indexOf(Object o) {
        int index = 0;
        if (o==null) {
            // header.element guaranteed null, no chance of looping past header
            for (Entry e = header.next; e.element != null; e = e.next) {
                index++;
            }
            // if index < size, null was found, else we looped to header
            return (index < size) ? index: -1;
        } else {
            for (Entry e = header.next; e != header; e = e.next) {
                if (o.equals(e.element))
                    return index;
                index++;
            }
        }
        return -1;
    }

Applying a similar transformation to lastIndexOf yields very pretty results:

    public int lastIndexOf(Object o) {
        int index = size - 1;
        if (o==null) {
            for (Entry e = header.previous; e.element != null;
                 e = e.previous, index--);
        } else {
            for (Entry e = header.previous; e != header && !o.equals(e.element);
                 e = e.previous, index--);
        }
        return index;
    }