I've constantly heard a protest being called by the manager of team (baseball, football, etc) who felt that there was an unfair ruling. Yet, after each of these games, the protest never goes through. Why is there a protest option in place, if it never works, or has it ever worked because in my lifetime, I've never seen it work.
In baseball, possibly the most famous game that was protested and resumed from the point of protest was the "Pine Tar Incident" game between the Yankees and Royals originally played on July 24, 1983. The game was replayed (again, from the point of protest which was 2 outs in the top of the 9th inning) on August 18th, 1983.
The last baseball game that where a protest was upheld was on June 16,1986 between the St. Louis Cardinals and Pittsburh Pirates, where it was argued that the umpires didn't wait long enough for a rain delay before stopping the game: http://www.baseball-reference.com/boxes/PIT/PIT198606160.shtml. It was resumed two days later.
Here is a list of baseball games that have been resumed due to protest, but the author acknowledges it might not be complete: http://www.retrosheet.org/protests.htm
The primary and overarching rule in any sports league is that the on-field staff is infallible. Even for booth reviews in football, the replay must show that the call was clearly wrong in order for it to be reversed (and that aspect of the ref's on-field ruling must be reversible; you can't, for instance, assert that a penalty should have been called when there wasn't one).
That said, most major leagues have adopted some sort of "appeals process", both in game and after the game is over. In some cases, rulings can be overturned on appeal even after the game is over, but in most cases, the spirit of the game and the assumption that "the referee is always right" still prevails, and the overwhelming majority of protests are unsuccessful on those grounds.
What a protest can change is the outlook of the officials. When shown that they made a bad call, officials learn from their mistakes even if there is no official action taken as a result of the protest. If the call was obvious enough and blown badly enough, the referee can be removed as incompetent and replaced for future games (I refer you to the Packers/Seahawks game and the controversial call that ended it; that was a major factor in getting the NFL owners to strike a deal with the officials' union and get the replacement officials off the field).
There have been a few cases in the German Bundesliga where games have been repeated because of so-called "phantom goals", where the ball missed the goal to the side but a goal was given nonetheless. You can (try to) read about these here: https://de.wikipedia.org/wiki/Phantomtor#Fu.C3.9Fball. It's dubious why these protests were allowed, but there you go.
Also, protests are routinely allowed (or at least considered) when they concern matters other than "facts connected with play" (which are final). For example, when ineligible players participated, or in case of fan violence, or perhaps in lower leagues if there are concerns about inadequate pitches or equipment. In these cases, if the protest is successful, games are typically awarded to the other side without a repeat. This isn't exactly a protest about an unfair ruling, which you asked about, but it shows why the protesting procedures exist.