Why does spiral or annular thickening occur in water conducting plant vessels?
Non uniform lignification of xylem vessels is beneficial to a plant in that it enables growth. It is at the unlignified parts of plants that growth occurs since fully lignified tissues are dead and so can not grow. Spiral and annular thickening allows for vessels to elongate and thus allows tissues to expand without breaking the vessel walls. 

Water cannot just go on flowing from plant cells because they are not lignified, plant cells have cellulose cell walls and cell membranes which prevent water loss. In addition, water in the xylem is not under pressure so I do not think water would be able to flow out of the xylem vessels except in cases where water is forced to move to adjacent phloem tissues by osmosis during phloem translocation.