It does seem odd from an American perspective, but in Japan, earning a driver's license is part of a complex system of licensing. Many students fail the test multiple times and for some of them, it is the only experience they have of being scolded by others. To get a rough idea of what counts, look at this wikipedia entry on licenss: http://ja.wikipedia.org/wiki/%E6%97%A5%E6%9C%AC%E3%81%AE%E8%B3%87%E6%A0%BC%E3%81%AB%E9%96%A2%E3%81%99%E3%82%8B%E4%B8%80%E8%A6%A7%E3%81%AE%E4%B8%80%E8%A6%A7 which gives all the licenses and this one http://ja.wikipedia.org/wiki/%E6%97%A5%E6%9C%AC%E3%81%AE%E6%A4%9C%E5%AE%9A%E8%A9%A6%E9%A8%93%E4%B8%80%E8%A6%A7 which lists all of the different types of qualifications offered by organizations and their corresponding tests. To get a vague impression of how vast and encyclopedic the Japanese qualification system is, look at shikaku-king.com which has everything imaginable under the sun, the pass rates, the price, and all sorts of other details.
What else to include? I am not entirely sure, and I will update this entry as I get feedback. I've won several minor prizes at conferences and a major scholarship from the Japanese government. I also have exceptionally high test scores. On an American CV, it would be odd to list my GRE scores or my LSAT score as a holder of a PhD. In Japan, however, it seems that many 履歴書 include things like TOEIC scores or 英検 qualifications. Consequently, I am tentatively including some exceptional test scores in my CV to prove that I am not merely a native English speaker but (at a minimum) a highly effective test-taker.
Like the TOEIC and 英検, you should include the 日本語能力検定 if you have it. Before writing a 履歴書 and researching the process, I never could understand the point of the JLPT tests beneath 2 (or for that matter 2). The only thing that really seems to have great impact is the JLPT 1. But now, I can see why it may be worthwhile to take the lesser (and more easily passable) tests -- this provides at least some proven qualification of limited Japanese competency. Alas, it is too late to pursue the JLPT 2 for July. Instead, I hope to take the JLPT 1 in December.
Right now, I am planning on the following section:
年 月 免許・資格
平成10 10 アメリカの○○○州普通自動車第一種免許 取得
平成14 10 LSAT 162点 取得
平成18 8 GRE Verbal 760点 Quantitative 800点 Writing 6点 取得
平成17 12 ○○○大学 教育失格
平成23 5 ハワイイ大学の上広学会のベスト ペーパー賞品
平成24 10 日本政府（文部科学省）奨学金留学生 研究生 取得
The 教育資格 is a certificate I received from my MA institution for taking a teaching course. While I would not say I greatly valued the class, I would say I learned things in it and it is precisely the sort of thing that seems to make sense when comparing with Japanese example 履歴書.