If your tile is an unfinished natural stone like slate, coral, limestone or travertine, you can get away with tiny grout lines because the tile itself is rough enough to prevent slipping. This isn't true if the tile is polished, or made of glazed ceramic or glass. Slick tiles provide a much more secure surface with 1/4-inch grout lines, because the rough grout acts much like adhesive traction strips, providing rough patches for your feet to grip.
The size of your tile also makes a difference in traction. Generally speaking, the smaller the tile, the smaller the grout lines can be without sacrificing safety. Mesh-backed 1-inch tile mosaics may have grout lines as small as 1/16 inch because the tiles themselves provide a rough enough surface to prevent falls. Tiles that are 10 to 12 inches are safest, with larger grout lines of around 1/4 inch, unless the tiles themselves are rough-textured. Four-inch tiles can go either way -- slippery materials should have grout lines of at least 1/4 inch, but rougher materials like slate would be fine with minimal grout lines.
The type of grout you use dictates your grout line limit, and your grout type is dictated by your tile. Glossy materials like glazed ceramic or glass do better with non-sanded grout, which can only be used when the grout line is 1/8 inch or less. Sanded grout is used for larger grout lines and provides better traction because of the rougher texture, but the sand grains can scratch glossy tile during installation. Using sanded grout with grout lines smaller than 1/8 inch will likely result in a messy finished product, because the sand grains make it difficult for the grout to fill the tiny spaces between the tile appropriately. This could lead to flaking over time.
If your tile is requires non-sanded grout but is too slick to provide much in the way of traction, you have a couple of options. First, you can use adhesive traction stickers -- many people have memories of the vinyl flower stickers on their grandmother's tub, but modern versions are more diverse and can be as unobtrusive as a series of individual dots color-matched to your tile. Alternatively, consider mixing up your tile pattern. Choose a smaller version of the wall tile, or intersperse your chosen tile with rows of 1/2-inch-by-4-inch tile bars that can provide traction and tolerate a larger grout line.