Who won the battle of the ironclads in Hampton Roads on March 9 1862?

On the tactical level, neither ship won. Both sustained minor damage, but neither was sunk. On the strategic level, the goal of the Confederate ship was to break the blockade and drive Union warships from Chesapeake Bay, and neither was accomplished. The day before the ironclads fought the Rebel ship had sallied forth and destroyed three wooden Union warships, but with the appearance of the Monitor the next day its effort against the conventional ships ended. Moreover, the failure of the CSS Virginia (or "The Merrimac" if you prefer) to lift the blockade, or to interfere with the Union operations underway, which involved landing troops from ships onto Virginia soil, cost the Rebel ship her anchorage. She drew too much water to be able to get over the bar into the James River, and so could not escape upstream, and had to be blown up by her own crew. So on the strategic level the Union was ultimately the winner, even though this was unclear at the time.