度(たび)にEach time, Every time, Whenever

Both おきに and たびに describe repeated occurrences, but are used differently. おきに attaches to time expressions to mean 'at intervals of (A)', e.g. '５分おきに電車が来る' ('Trains arrive every five minutes'). たびに describes a response that recurs whenever a particular thing happens, e.g. '見るたびに笑ってしまう' ('I end up laughing every time I see it').

ごとに and たびに both express frequency, and can be interchangeable in cases like 失敗するたびに／ごとに 'every time (you) fail'. However, ごとに can directly follow time or distance expressions (e.g. ３時間ごとに), while たびに requires a verb indicating an action or event, e.g. ３時間が経つたびに 'every time 3 hours pass'. Their noun forms also differ, e.g. 発表の度に vs. 発表ごとに (both meaning 'with every announcement').

Both まい～のように and たびに express frequency and the idea of 'every,' but with different nuances. まい～のように is used with 'every~' time expressions to mean 'almost every (A)', e.g. 毎日のように 'almost every day'. In contrast, たびに follows verbs or noun phrases to mean 'every time (A)', e.g. 彼に会うたびに 'every time I see him' or 旅行のたびに 'every time I take a trip'.

These are similar expressions that both express the idea that every time one thing happens, so does something else. While they are interchangeable in some cases, につけ can only be used for naturally occurring events, e.g. '見るにつけ笑ってしまう' ('I laugh every time I see it'). たびに can also be used for volitional actions, e.g. '出張に行くたびにお土産を買う' ('I buy souvenirs every time I go on a business trip').