A few additional points worth noting:
  • The address can be written in a number of different ways. The style of thbz's example is mildly old-fashioned, these days the standard style would be the more concise Akasaka 8-10-32, prepending the chome. In Japanese, the dash is read (and can be written) "no", meaning "of" (8 of 10 of 32). This is vaguely analogous to DNS. An apartment number can also be suffixed, eg. I used to live at Komaba 4-6-29-508. Alternatively, you can expand the address all the way: Akasaka 8-chome 10-cho 32-ban.

  • The ordering of the address bits seems highly random at first sight, but this is an illusion caused by the incompatibility of the Japanese and Western systems. In the West, addresses go from specific to general -- name, number, street, town, country -- whereas in Japan the order is cleanly reversed. Thus, in Japanese, the address above would be Tokyo-to Minato-ku Akasaka 8-10-32, which fits quite nicely on one line when written in kanji. Alas, this gets mutated in all sorts of bizarre ways when mapped to romaji and massaged so that gaijin postmasters can deal with it.

  • While the ordering by construction date makes finding addresses in the older parts of town fiendishly difficult, newer planned suburbs will quite often be very nice and logical. Some massive apartment danchi -- the miles-long concrete wasteland near Funabashi, Chiba comes to mind -- even have the numbers stenciled on them in 5-meter-high letters.

  • The length of an address is a good indication of how urban the area is. A 4-6-29-508 is obviously an apartment in a heavily built-up suburb, whereas a mere 4-6 is almost certainly in a smaller town. By the time the area name is trailed by a single number, you can be sure that the nearest neighbors are rice paddies and mountains.