Buying amulets, fortunes, goshuin
Shrines often sell amulets, known as omamori, which protect the wearer against various ills while also bringing them good fortune. Shrine visitors can also buy an omikuji or fortune, written on strips of paper that can be either good or bad. If you get a negative fortune, it is a common custom to tie the paper to a nearby tree branch or wire so the bad luck stays behind when you leave the shrine.
Many visitors also enjoy collecting goshuin (stamps) from each shrine they visit. They can be anything from an actual, simple stamp to a hand-inked calligraphy message from the shrine priest. Goshuin are often kept in a special book called go-shuincho, which you can buy at the shrine itself or a stationery store. Some goshuin are free, but at some shrines, you may have to pay a fee of around JPY300-500 to get it.