* hiragana (ひらがな): A syllabary with 46 characters representing syllables.
* katakana (カタカナ): Another syllabary, also with 46 characters, used for emphasis, foreign words, and onomatopoeia.
* kanji (漢字): Logographic characters borrowed from Chinese, each representing a word or morpheme. There are thousands of kanji, but a relatively small number are used regularly.
So, while there are not "alphabets" in the traditional sense, there are three distinct writing systems used in Japanese.