The other day I heard someone say "Jiminy Christmas", I had not heard the expression in years. I started wondering what it really meant, Google found the origin and meaning: someone perhaps thought an expression chosen to PREVENT swearing was appropriate.)"Jiminy Christmas" is much rarer than, and almost certainly derived FROM "Jiminy Cricket" -- both being "minced oaths" to avoid outright swearing by yelling "Jesus Christ" in what's considered a disrespectful or 'profane' manner. (I'm not sure whether it was originally singular or plural, though "crickets"does SOUND more like "Christ"...At any rate, Disney's use has established the singular.)
In fact, minced oaths for the names of God and Christ, and other terms connected with the sacred, or with eternal judgment, have been a common thing for centuries. More recent cases are based NOT on religious terms (which many people are less bothered about profaning in modern times), but "vulgar"/objectionable terms (the sort Yahoo!Answers turns into asterisks -- e.g., "shoot" and "freaking") They've been formed in many different ways, but one common method is to take the first part of the original word and substitute some other ending, perhaps very similar to the original. . or not. The final word MAY be a real word (like "cricket"), or complete nonsense. Other minced oaths are formed by rhyming. Jesus Christ - Jeepers Creepers, Judas Priest (in this case the LAST part of "Christ" is matched)Jesus - Gee whiz, Gee, JeeshChrist - Cripes or Cripes sakes (for "Christ's sake") CRIMINY (though in this case it starts with the sound of "cry"). Yes, it appears that"Jiminy" and "Criminy" are related. "Jiminy", it seems, came first (attested 1803)-- and was at first used by itself The Online Etymology Dictionary suggests the expression is based on Latin "Jesu Domine" (domine meaning "Lord")--using the first and last parts. "Jiminy Cricket" is first attested later (1848).
Looking at some other minced oaths. Here's a very partial list, with a few notes --
(by) God - (by) golly [perhaps also influenced by "holy"], Gosh, by Jove, egad (O God),damn - dang, darndamnation - tarnation God damn -dadgum (note that this one is based on exchanging the first part of each word gu- da- ) hell - heck