Most Japanese websites use default font sets provided on Windows, Mac or Ubuntu. The latest ones are Meiryo, Hiragino Kaku Gothic Pro and Noto. For older versions such like Windows XP, it is good to add former default fonts MS Gothic(or MS Mincho)/Osaka. Older Linux versions may include Takao fonts.
Some old browsers could not understand those font names in English, some others do not recognize the names in Japanese, so it is safe to write both in Japanese and English.
Meiryo and Hiragino's order is, because Mac users may have Meiryo from MS-Office, and Hiragino is more familiar and matching well on Mac, better by starting Hiragino series.
So the current recommended practice is like this:
font-family: "ヒラギノ角ゴ Pro W3", "Hiragino Kaku Gothic Pro", Osaka, メイリオ, Meiryo, "ＭＳ Ｐゴシック", "MS PGothic", "ＭＳ ゴシック" , "MS Gothic", "Noto Sans CJK JP", TakaoPGothic, sans-serif;
Source: http://stackoverflow.com/a/14573813/4335961. Updated with Ubuntu fonts.