Attaches to nouns, counters, or verbs to express 'each time', 'every', or 'per'. With time/distance nouns it means 'at intervals of'. With verbs it means 'each time one does'.
This train departs every 10 minutes.
He greets each person he meets.
Different flowers bloom each season.
ごとに marks the unit or occasion itself (each time/per unit), whereas ずつ distributes a fixed quantity evenly, as in 一人に一つずつ (one each per person).
毎に is the common adverbial form used before verbs to mean 'each time', while 毎 is the bare suffix attached directly to a noun to mean 'each'.
度に means 'every time (something happens)' and focuses on a recurring event, while ごとに means 'every' in the sense of regular intervals or individual units (年ごとに, 家ごとに).
ごとに is the plain way to say 'per/each', matching に付き's distributive 'per' sense but without its formal, business-document tone.
Derived from the noun 毎 (ごと, 'each') + particle に. The kanji 毎 is used for 'every' or 'each', but the kana form ごとに is now standard.