we keep our grown up games in the top closet shelf in our guest bedroom because we don't play them as much.
but the kids board games, puzzles and card games etc are on a low, deep 3 shelf book shelf in the family room, keep all puzzle pieces in ziploc bags in the boxes, if the box gets trashed, I cut the pic of the puzzle and put it in the baggie too, then it goes in a puzzle basket. I keep all the card decks, small hand games etc in a basket there too. its been working great for awhile now for my 4.5 and almost 7yo, and can stay pretty tidy and organized looking. I'll have to come up with something else in not too long though, I'm sure my 7week old will love to pull and dump in that area in a few months