In English media, the word "regime" is almost exclusively used to describe dictatorial or repressive governments, eg "the Soviet regime", or by political commentators when describing a government they don't like.
Both "regime" and "government" are borrowed from French, and have similar origins, so why does "regime" have a more negative connotation, and when did this difference in usage start?
The term régime, in its political sense, didn't enter the English language until the French Revolution and it was mainly associated with the notion of the the Ancien régime: the political and social order that preceded the Revolution. As a consequence, it tended to have the connotation of a political order that was corrupt, antiquated, illiberal, and on the verge of collapse - although it was not always used in this sense.
By the 20th century, the meaning of the term also took on the more specific connotation of a ruling group, retaining this pejorative association with authoritarianism. Thus one magazine in 1918 wrote that "How many men, women, and children the Bolshevik regime has slain or starved to death, the world does not yet know." Or The Times of London wrote in 1955, "None of us is prepared..to bolster up the aging régime of Chiang Kai-shek."
So the negative connotation already existed to some degree when the word entered the English lexicon in the last decade of the 18th century, but in the 20th century its meaning was extended to various authoritarian governments (whether communist, fascist, or otherwise dictatorial).
Source of quotations: Oxford English Dictionary