Gravity affects tile just as much as it does any other material, and with large-bodied tiles, this is especially true. For most projects you can expect to use at least a 1/2-inch notch, although especially large tiles may require a 3/4-inch notch because more thinset is needed to cushion against gravity as well as provide sufficient support for larger tiles.
Just as important as the trowel size is the type of thinset you use. For traditional thinsets, you want to use as little thinset as possible, so a 3/8-inch notch might work for a 14-inch tile while a 1/2-inch notch is used for anything larger. However, when you use specialty non-sag thinsets that are designed to help with gravity, you can use a larger notch to provide extra coverage.
Natural stones are generally heavier than any type of ceramic or porcelain. In addition, the thickness of the stone is not always uniform. Extra thinset helps cushion the natural stone pieces such as granite and marble in a thick bed of mortar that allows you to adjust the face of the tiles until perfect flatness is achieved. You should always use a 3/4-inch notch for anything over 18 inches and a 1/2-inch trowel for 16-inch pieces.
Thinner than natural stones and considerably lighter, ceramics and porcelains do not require as much thinset. A 3/8-inch trowel is generally sufficient for pieces up to 16 inches. Anything larger should use a 1/2-inch trowel to provide sufficient thinset for the tile to bond with. However, you should always check the coverage on a random piece to ensure that you have enough mortar as larger pieces need entire coverage.