The Japanese writing system consists of three main components: hiragana and katakana (collectively known as kana), and kanji. Arabic numerals are often used instead of traditional numerals. Occasionally Latin characters are used for effect. Rōmaji is used to phonetically transcribe Japanese into a Latin-only alphabet.
Kana each consist of 46 basic symbols representing syllables, along with a few diacritics to to extend them.
Hiragana (平仮名 – ひらがな – ヒラガナ), which has a more rounded or cursive style, is used primarily for syntax and grammar markup, native words that don’t have kanji, and to annotate or substitute for less well known kanji.
Katakana (片仮名 – かたかな – カタカナ), which has a more angular style, is used primarily for words of foreign origin (other than Chinese), non-Chinese/Japanese names, and for emphasis (similar to the use of italics in English).
Kanji (漢字) are Chinese characters. They are used for their meanings, for their sounds, or both. This is highly context dependent, so a single character may have several (in some cases over 10) radically different “readings”; thus the need for furigana or rubi, the tiny kana annotations you sometimes see above or beside kanji.
Basic literacy requires knowing about 2000 kanji, specified by the government as part of the school curriculum. Well-educated adults tend to know 1-3000 more. There is a separate, smaller but overlapping list of kanji which are approved for use in proper names.
Rōmaji (ローマ字) uses the Latin alphabet to write Japanese phonetically. It is primarily used for foreign readers and computer input (the input method software converts it into “real” Japanese characters). While the most common romanization system is Hepburn, several others exist; collections of older documents in particular show a greater variety in spelling.
2009-12-04: added Kana chart