Something that's fun to collect as you travel Japan are stamps. You may not notice them at first, because they may be hidden in a corner, but many tourist attractions, train stations, and even subway stations have a stamp. I carry a small (3.5 inch wide) unlined Moleskine notebook for this purpose.
This stamp is from the Naruto Station in Shikoku.
The stamp reads:
The station of famous roaring whirlpools.
Naruto National Park
Naruto Rail Line, Naruto Station
Along the bottom is a space for the year, month, and date.
You will find these stamps in various conditions. Sometimes the stamps are self-inking, or there may be a fresh ink pad, but other times the stamp may be worn or the ink pad dried out. If you're really a fanatic you can bring one or more ink pads with you. If the color you have doesn't match the color of the pad currently in use, you may want to wipe down the stamp before and after use, as a courtesy to others. Also, remember to close the ink pad lid when you're done, so doesn't dry out!