The biggest reason we have the current system of binding primaries and caucuses is because the 1968 Democratic nomination process was a total balagan. We have a sitting Democratic president running for reelection--one who's even done quite good stuff in his Great Society Program and on the Civil Rights front, but whose escalation in Vietnam is unpopular particularly with the youth--and he totally gets "primaried" by Eugene McCarthy in New Hampshire before getting primaried was even a thing. McCarthy's campaign was a grassroots effort mainly by anti-War young people, who "got clean for Gene" and went door to door in New Hampshire before going door to door in early primary states was really a thing. Lyndon Johnson actual won in New Hampshire, 48% to 42%, but that's not the kind of result you see from a sitting president so by the end of the month Johnson says he will not seek or accept renomination.
Gene McCarthy won the battle (sort of) but lost the war, and LBJ's resignation set off a scramble in Democratic politics. RFK steps in soon after NH but he is assassinated a few months later, in June, before the Democratic Convention. As you can see from the map on Wikipedia, in 1968 most states did not select pledged delegates through caucuses or primaries, but had various other means (usually closed to the public) of selecting who to send to the convention. Also, this was still a period when presidential candidates could be picked in the notorious "smoke-filled rooms".
And that's what happened. Despite not winning a single state (though some of his surrogates did--it was a different time and one could have surrogate "favorite sons" on the ballot), the convention chose Hubert Humphrey, LBJ's vice president, instead of Eugene McCarthy or anyone else. This caused a lot of controversy, including the infamous Convention in Chicago which was marred by protests and "a police riot". Humphrey's strategy focused on getting delegates from non-primary states, and in the end--with RFK's assassination getting rid of the other quasi-"establishment" candidate--it was a successful one. Even before RFK was killed, Humphrey was leading the delegate count (though RFK+McCarthy had more). At the actual convention, Kennedy's various candidates didn't vote as a block, and Humphrey was able to win. Many people--not just the radical anti-War protestors in Chicago--didn't like this, and the whole system was reformed. Here are two posts about that:
The US is just starting presidential primary season. The modern primary and caucus system only dates back to the 1970's. Why did both parties switch at the same to the new system? How did this change happen? (this was actually my own question, but read the OP and the three comments)
So modern primaries only date from, at the earliest, 1972. Super delegates were only really added to the Democratic side before the 1984 primary process. The 1982 Hunt Commission added them because the Democratic establishment was unhappy that in 1972 and 1976 two "factional" candidates won. McGovern won by clever focusing on early primaries and pledged delegate counts and managed to eke out victory at the convention despite having a narrow, liberal, anti-War base. He got clobbered by Nixon in the general. Jimmy Carter, who won the primary process in 1976 and was renominated in 1980, won the primary process by scoring media attention through early wins (something that everyone does now) and sweeping the South. The Hunt Commission suggested 30% unpledged, party-picked delegates, but party eventually went with 14%. This has been increased and now super delegates on the Democratic side make up 20%. They're a lower number on the Republican side, as the Republicans didn't have the same problem with factional candidates as they were developing the modern primary rules. I think they're about 7% of Republican delegates currently, though I don't know if this number has been consistent. To my knowledge, they've never been deciding in an election. It looked like they might be important in 1984, but Hart lost several key states on Super Tuesday, which put Mondale over the top (he was leading in Superdelegates already). Mondale, who got the nomination, got whomped by Reagan almost as bad as McGovern got whomped by Nixon--both only picked up one state.
In 1988, once Hart was crippled by scandal (the first major Americna political sex scandal of the modern era), Dukakis ran away with it. In 1992 Clinton ran away with it, and was reelected in 1996. I'll be exceedingly brief post 1996 to avoid infringing too flagrantly on the 20 year rule, but no, it never happened since then either. In 2000, Clinton's vice president Al Gore ran away with it. In 2004, Dean led the early super delegate counts but once people actually started voting, Kerry won almost every state. In 2008, people again thought the super delegates would matter, considering Clinton's early lead in them but a tight race otherwise, but in the end, as Obama was taken a clear lead in the pledged delegates, he also started taking a clear lead in the unpledged delegates. You can see that from the graph here.
On the Republican side, Reagan ran away with it in 1980 (after being a strong challenger in 1976 against the sitting Ford) and was renominated in 1980. Bush, Reagan's Vice-President, ran away with it in 1988 and was renominated in 1992. Dole, Bush's strongest opponent in 1988, ran away with it in 1996. In 2000, it wasn't as clearly someone's "turn" as it had been in the last several cycles (Dole's opposition--the paleoconservative Buchanan and the fiscal conservative Forbes--were both seen as highly factional candidates), but George W Bush triumphed convincingly over McCain and was renominated in 2004. In 2008, despite losing Iowa badly, McCain managed to go the distance and convincingly beat his challengers, Romney (who failed to beat McCain in moderate Michigan) and Huckabee (who failed to beat McCain in conservative South Carolina). In 2012, despite a lot of early fluctuations in his opponents, Romney carried it almost wire to wire (though it took him longer clinch the nomination than some expected after late, strong showings from Gingrich in the South and Santorum in the Midwest).
So, no, since the debacle of the 1968 Democratic Convention which gave rise to the modern primary rules, Super Delegates (the Republicans use a different word, IIRC, and are by all counts much less important, but conventionally they're also customarily referred to as Super Delegates still in the media) frequently been a hypothetical factor, some times discussed heavily in the media, but have to my knowledge never once been an actual factor in choosing a party's nominee at the convention. The 2008 and the 1984 Democratic primary seasons were when there was the most speculation about their possible role of their role, since those were also the two elections where the nomination process was up in the air the longest and delegate counts the closest. However, even there, they didn't actually make a difference.