The napkin can add a lot to your tabletop. The flat fold (vertical and horizontal) and pocket fold have been very popular for holding menus and other items.
But there are some other traditional folds that can be updated. Like the rose fold. This would look great in a taffeta or pintuck fabric holding an orchid, or peony, or a favor!
The slide fold is crisp and modern - perfect to lean a place card or program against.
It is important to consider napkin fabric when selecting a fold. Cotton, linen, and silk hold up best for more intricate folds. Softer fabrics like satins and silks make beautiful pockets or flat folds. There are many books available with updated folds. We found these standards at Napkin Folding Guide