Regex for matching ALL Japanese common & uncommon Kanji (4e00 – 9fcf)
([一-龯])

Regex for matching Hirgana or Katakana
([ぁ-んァ-ン])

Regex for matching Non-Hirgana or Non-Katakana
([^ぁ-んァ-ン])

Regex for matching Hirgana or Katakana or basic punctuation (、。’)
([ぁ-んァ-ン\w])

Regex for matching Hirgana or Katakana and random other characters
([ぁ-んァ-ン！：／])

Regex for matching Hirgana
([ぁ-ん])

Regex for matching full-width Katakana (zenkaku 全角)
([ァ-ン])

Regex for matching half-width Katakana (hankaku 半角)
([ｧ-ﾝﾞﾟ])

Regex for matching full-width Numbers (zenkaku 全角)
([０-９])

Regex for matching full-width Letters (zenkaku 全角)
([Ａ-ｚ])

Regex for matching Hiragana codespace characters 
(includes non phonetic characters)
([ぁ-ゞ])

Regex for matching full-width (zenkaku) Katakana codespace characters 
(includes non phonetic characters)
([ァ-ヶ])

Regex for matching half-width (hankaku) Katakana codespace characters 
(this is an old character set so the order is inconsistent with the hiragana)
([ｦ-ﾟ])

Regex for matching Japanese Post Codes
/^¥d{3}¥-¥d{4}$/
/^¥d{3}-¥d{4}$|^¥d{3}-¥d{2}$|^¥d{3}$/

Regex for matching Japanese mobile phone numbers (keitai bangou)
/^¥d{3}-¥d{4}-¥d{4}$|^¥d{11}$/
/^0¥d0-¥d{4}-¥d{4}$/

Regex for matching Japanese fixed line phone numbers
/^[0-9-]{6,9}$|^[0-9-]{12}$/
/^¥d{1,4}-¥d{4}$|^¥d{2,5}-¥d{1,4}-¥d{4}$/

Update from 2014 by user cb372
Hiragana = [ぁ-ゔゞ゛゜ー]  // 0x3041-0x3094, 0x309E, 0x309B, 0x309C, 0x30FC
Katakana = [ァ-・ヽヾ゛゜ー]  // 0x30A1-0x30FB, 0x30FD, &#x30FE, 0x309B, 0x309C, 0x30FC
Hiragana or katakana = [ぁ-ゔゞァ-・ヽヾ゛゜ー]  // 0x3041-0x3094, 0x309E, 0x30A1-0x30FB, 0x30FD, &#x30FE, 0x309B, 0x309C, 0x30FC

Update from 2019 by user minhloc2011
Just updated full-width Katakana from「30A1」～「30FE」 (Unicode：30FB).
Regex for matching full-width Katakana (zenkaku 全角)
([ァ-ン])
Replace to:
([ァ-ヾ])