The creature blocks only if it's able to do so as the declare blockers step begins. If, at that time, the creature is tapped, it's affected by a spell or ability that says it can't block, or no creatures are attacking its controller or a planeswalker controlled by that player, then it doesn't block. If there's a cost associated with having the creature block, the player isn't forced to pay that cost. If that cost isn't paid, the creature won't block.