Unmissable Japan has catalogued Fifteen Amazing Japanese Footbridges. Since we’ve only visited one of these, we’ll simply rip off their work with a link here.
Part of the fascination of Japan is not only that these bridges are preserved, but that they’re actively maintained, in many cases open to traffic (or at least tourism), and they’re catalogued and featured in regional tours. Nana and I have been on the Iya Valley Bridge (pictured above) as well as a couple of other suspension footbridges not included in the article, as part of package tours (although Nana has been overheard shouting イヤー、イヤー while crossing them).
Japanese being who they are, the bridges collected in this article represent more than antiquity — in many cases they are unique engineering solutions to local circumstances. See for example Nagare bridge, whose bridge surface is designed to float in order to avoid damage to the pylons during a typhoon, and the Tsujun aqueduct, which irrigates higher adjacent land via siphons.