Rare. Despite lots of "stories, " the truth is severe complications (abcess, permanent injury) are very rare. And the reputation that epidurals can cause chronic back pain has been disproven in multiple studies...The actual cause is really from the pregnancy itself, or the weight gain (or lack of weight loss after the pregnancy).
Head ache. But its still a rare complication. Less than 5%. Other even rarer complications are infections at the site of needle placement or infection or inflammation further in the tissue that surrounds the nerves. Again these happen with very low incidence. One must always balance the risk vs benefit of any procedure.