Cut the caulk along the top edge of the baseboard with a utility knife. Cut along the entire length of the baseboard. This will ensure you don't tear the drywall paper when removing the board.
Set the blade end of a stiff putty knife down into the gap where the caulk was cut, at one of the ends of the baseboard. Hammer the putty knife blade down between the baseboard and the drywall until the gap widens to about 1/4 inch. Keep the handle flush against the wall to keep the blade from cutting into the drywall.
Slip the angled end of a flat pry bar down into the gap. Place a 6-inch-long piece of baseboard between the wall and the pry bar. Lift the pry bar handle up toward the wall until the bar connects with the piece of baseboard. Continue prying up until the nails holding the baseboard to the wall pull out of the drywall. The 6-inch piece of baseboard will keep the pry bar from damaging the wall. Repeat this process along the entire length of the baseboard.