Today, the congress of Venezuela granted their president the power to rule by decree, essentially making him dictator for 18 months - and likely until he is replaced by force.
Such actions are not unprecedented, of course. Perhaps the most famous case of a democracy voluntarily turning itself into a dictatorship is the German Enabling Act of 23 March 1933. While it technically granted powers to the cabinet, in practice it granted dictatorial powers to the Chancellor.
Many feel that the strength and long term stability of the United States' government is rooted in its being a democracy. I disagree. Democracies have been repeatedly shown to be highly vulnerable to charismatic and unscrupulous politicians.
Rather, the strength of the United States' government is rooted in its being a constitutional government, with a constitution that is difficult, though not impossible, to amend. The balance achieved by the U.S. constitution's amendment process, not democracy, is what has permitted the nation's government to remain largely stable for over two centuries.
In political science, the definition of "democracy" usually includes not just elections, but institutionalized protection of minority rights (e.g., speech, assembly, religion), an independent judiciary, etc. Then "democracy" is a subset of "majoritarian" systems, i.e., all systems with majority rule, including those without all the protections we have in our constitution.
It's an important distinction, as you note. Venezuela is only the latest in a string of disasters. Pakistan is a classic case of what goes wrong when you have elections without the rest of the institutional support for a genuine liberal democracy; you get repeated military coups that actually improve the situation.
We came dangerously close in 1936, when Roosevelt threatened to appoint six new judges to the Supreme Court. Subversion of the separation of powers is likely to be a pretty good warning sign of a threat to liberal democracy.
The Roman republic had an interesting procedure for appointing a dictator to a 6 month term in the event of a national crisis - and in fact it worked well for quite a long time, with most of those dictators actually resigning before completing the term.
(Also interesting is that the dictator was the only Roman office held by only one person at a time - every other position had at least two simultaneous officeholders to provide checks, and that the dictator was the only Roman official to have immunity from prosecution for acts committed while in office).
Of course, eventually Caesar was declared Dictator-in-Perpetuity, and that was it for the republic.