Most people familiar with Japan are aware of the Japanese birth-order naming system for males, whereby first sons are often called 一郎・太郎 Ichirō/Tarō; second sons 二郎・次郎 Jirō; third sons 三郎 Saburō, and so on. In theory, it would be possible to keep going up to at least the tenth son: 四郎, 五郎, 六郎,七郎, 八郎, 九郎, 十郎. However, I'm not sure how to pronounce the characters for fourth son, can't find it in my dictionaries, and suspect that it would be an extremely unlucky name because Sino-Japanese shi 'four' sounds like shi 'death'. (Japanese high-rises often lack a 4th floor, for the same reason that my high-rise condo in the U.S. lacks a 13th floor.) [See the correction below.]
Another thing I'm not so sure about is whether this system marks order of issue or order of survival. Back in the old days, many more children died very young. That might account for the naming of Admiral Tōgō Heihachirō, whose name (東郷 平八郎) suggests he might have been his mother's eighth son, even though he had only three brothers as an adult. (My farm-raised father's eldest brother and eldest sister also died very young, but he still ended up with five brothers and one sister.)
Birth-order naming systems are also very common in the coastal languages of the Huon Gulf of Papua New Guinea. The naming system in Numbami accommodates up to seven sons and five daughters, and without incorporating any numerals. The order-of-issue names for sons are Alisa, Alinga, Gae, Alu, Sele, Dei, Ase Mou; and for daughters are Kale, Aga, Aya, Damiya, Owiya, Ase Mou. Notice how the names for the seventh son and sixth daughter are the same? That's because both translate as 'name none', or No-Name. My host mother during my fieldwork had seven sons and four daughters, all of all of whom survived thanks to postwar improvements in public health. The youngest son was called Ase Mou 'name none', or Ase 'name' for short. Of course, as the kids get older, they tend to go by their baptismal names (often of Biblical origin) or traditional names, depending partly on whether they remain in the village or move to town.
Another coastal language for which birth-order names have been recorded is Labu, which is the only surviving coastal member of the Markham subgroup, which stretches far inland up the Markham River valley. The Labu names for the first five sons are Aso, Amoa, Aŋgi, Aŋgu, Ôlôndi; and for the first five daughters are Ami, Hiya, Aya, Êta, Hênamu. (My source seems a little bit confused about the names farther down the line.) If you compare the Numbami names to the Labu names, only the names of the third daughter match. (However, I'm guessing that Labu Asôlô for both males and females toward the bottom of both lists is the etymological equivalent of Ase Mou 'name none', even though the current Labu word for 'name' is apaŋa.)
This is typical of the Huon Gulf Sprachbund: the structures match but the sounds often don't. That facilitates translation, but not lexical retention. Fortunately, human memories can retain enormous amounts of lexical clutter; while human brains are much less efficient at quick translation between languages. (Human RAM far exceeds human CPU capacity. The rise of transformational grammar seems to have been predicated on the opposite assumption: People had to derive one semantically related structure from another; they couldn't memorize both and then analogize between them.)
UPDATE: For Japanese kanji jocks (or kanji bandits), Matt of No-sword offers some interesting observations of how people have simplified characters by employing ditto marks (or means very similar). Sort of a calligraphic compression algorithm.
CORRECTION: (Slaps forehead.) Matt corrects me (and not for the first time). 四郎 Shirō is neither unlucky nor uncommon. Well, it's less common than 三郎 Saburō but more common than 五郎 Gorō for the same reason that third sons are more common than fourth, and fourth more common than fifth. Instead of puttering around in my kanji dictionaries, I should have googled up likely names like Suzuki/Tanaka/Yamada Shirō.