It is not necessary to finish a wood deck. Without paint or stain, a deck will naturally check and turn shades of grey, but it will remain structurally sound.
So if that Old World look is right for you, then enjoy (watch out for splinters, though)! If you like the look of painted wood, go ahead and paint your deck.
Once you do it, though, you must stick with it for the life of the deck. If you later decide to change to a natural look, the stripping and sanding necessary to remove paint can be more expensive than putting in a new deck!
To protect your deck from rotting and splitting without painting, consider staining your deck a natural color or applying a penetrating clear sealer–not a topical product–to protect it from our brutal sun’s harmful rays. Once you stain or paint it, though, you’ll need to redo it every year.