Show entry on certain date, regardless of year
I fear this is not possible with a simple postDate parameter and you have to find a workaround.
The Twig apporach would be to loop all events and filter the right ones with a simple conditional.

{% set events = craft.entries.section('events').limit(null).order('postDate asc') %}
{% for event in events %}
    {% if event.postDate|date('m-d') == now|date('m-d') %}
        ...
    {% endif %}
{% endfor %}


If you'd like to paginate the results, collect / merge entry IDs within the for loop first and
then prepare another ElementCriteriaModel with these IDs in its id param, to get the entries.