Reboots, Reality Shifts, and Retcons
Add to these universes ones where heroes and villains swapped, universes for characters from companies DC Comics had acquired, etc. and DC felt their continuity had become convoluted. Their solution was Crisis on Infinite Earths, a 12-issue series was designed to simplify things, combining all these universes into one. Great battles took place, with entire universes being destroyed and a new universe was created, largely from Earth-1, but with elements from other universes. The heroes of the 1930s and 40s still existed unless that character's incarnation was still in use, in which case the hero was removed from the "Golden Age" era of the 30s and 40s. For example Superman was established to have begun his career a few years ago as did the Barry Allen Flash but the Jay Garrick Flash still existed from the 30s and 40s - and was still around, albeit semi-retired. Many of the Golden Age characters were explained to have had exposure to some magic anti-aging effect used to justify how despite their early adventures actually having a definitive date they were still in excellent physical shape, typically being portrayed as no older than late middle age.
Given all this tweaking, the editors decide this would be a fine time to revisit the origins of their classic characters. For example Superman's backstory was changed such that he was never Superboy and his parents were stil alive. This had some nasty side-effects - much of the history of the 30th century Legion of Superheroes involved time travel allowing them to have adventures with Superboy. A modification Hawkman's backstory made a number of comics actively being published an apparent contradiction. It became difficult to know if a given story from the past ever happened and if it did if it had any changes. DC dealt with this by having additional "crisis crossovers" which made additional changes to the universe, re-introduced in a limited way the concept of parallel Earths, and made additional changes to the backstories of heroes.
Finally DC had a crossover known as Flashpoint which, at the end, redid the universe yet again, leading to DC's New 52. All comics were reset to issue 1. This included, rather surprisingly, some comics whose numbering was beginning to close in on an issue 1,000, having been in continuous publication since the 1930s. Some heroes have had large changes to their backstory - for example, the marriage of Clark Kent and Lois Lane was eliminated - actually it now never happened. On the other hand, the main Green Lantern comic book continued pretty much where it left off, albeit with a new focus based on what happened previously.
DC Comics is probably the best known entity to have done such operations in retroactive continuity though they are by far from the only one. Marvel has tended to avoid radical retroactive redefinitions to their universe wholesale, though one notable exception was the "One More Day" storyline in Amazing Spider-Man, where Peter Parker, alter-ego of Spider-Man, and his wife, Mary-Jane, made a deal with the devil to undo their marriage in exchange for saving the life of Peter's elderly Aunt May. This was met with a great deal of unhappiness by the fans. I'll be talking about reactions to retcons below but I'll touch on this one specifically. The issue that Marvel editor-in-chief Joe Quesada wanted to deal with is they felt Peter Parker's marriage inhibited storytelling potential. I don't necessarily agree with that assessment - I think not having story potential due to marriage is a bit of a cop-out but even assuming that to be the case, the solution was very inelegant. It was a retcon that Peter Parker chose for himself. Though he loved his aunt, it is difficult to believe it is what she would want for him - heck she was the one that pretty much shoved Peter into having a date with her. But moreover the "deal with the devil" aspect of this was particularly unsatisfying. It is true that some marriages do not work out and it would seem a divorce would be a more reasonable solution than a deal with the devil. As I understand it Marvel was hesitant to have Peter Parker get divorced, not liking the stigma of it, but a deal with the devil seems a lot less acceptable. It's a difficult balancing act - on one hand they wanted Peter to make a choice and his whole motivation for being a superhero was his failure to stop a criminal led nearly directly to his uncle's death - so it is easy to understand how much he would want to save his aunt. But the choice he made just... it left a very bad taste in my mouth as a reader and I imagine others felt similarly.
Moving outside of comics into films and television we find retcons to be less prevalent. There what seems to be the new trend is that of a "reboot". An example of this is the Batman films of the 80s and 90s followed by the modern Batman Begins/The Dark Knight/The Dark Knight rises series. On one hand a reboot can make some sense if a series left on a bad note or it has been a long time since the last installment. On the other hand it can be overdone - for example it seems rather odd for Spider-Man to be getting rebooted so quickly.
One technique that I was particularly fond of was the one Doctor Who took when it returned to television after not being a regular show for over 15 years (with a single made for TV movie in that gap). Doctor Who simply continued but did so in a way that did away with a number of continuity concerns. The original television series delved into a lot of backstory involving the Doctor and his people, the Time Lords. The new series added a new backstory where the Doctor's people were wiped out in a Time War with the Daleks. The Doctor was shown to be able to regenerate into a new incarnation (and new actor) in the previous series so this series started with a new actor as the Doctor - but it did not even mention regeneration until that actor departed. The new show was largely from the perspective of his companion Rose who was a stand-in for the audience who knew nothing about all the backstory of Doctor Who. And the show was careful to not expect detailed knowledge of previous continuity - if something from the original show was introduced it was introduced in such a way that it could be explained to someone who knew nothing about that thing. Doctor Who is an unusual case in that its premise as a time travel show allowed the removal of the Time Lords as something absolutely appropriate to the concept - indeed in the original show the Time Lords were shown attempting to wipe out the Daleks before they ever existed. This technique was very wise in my opinion - the made for TV movie involved lots of "info-dumps" to explain all sorts of things. It started from the perspective of the Doctor vs. making use of a human stand-in for the audience.
Some games upon changing editions, even if those changes did not involve "reality shifts", make massive changes to the background. For example, in the Traveller RPG the default setting is the Imperium, an empire which rules much of known space. The next edition of Traveller, MegaTraveller did not introduce large changes in the rules but rather added lots of details and new rules while leaving much of the core intact. Despite that the default setting changed to that of the Rebellion - a massive civil war as various factions formed trying to claim the throne of the Imperium. A larger change to the rules in Traveller: The New Era advanced the timeline of the default setting even further, making it into something of a post-apocalyptic setting with a sentient computer virus wreaking havoc on civilization.
When dealing with non-interactive entertainment my reaction to retcons, reboots, and the like is variable. If I was actively following a series and was quite happy with it my reaction to the change is less likely to be positive. An example of this was what was done in Spider-Man. I was greatly enjoying the storylines that were taking place. Not only was Peter Parker's marriage undone but major changes like his public revelation of his secret identity was undone as well. Moreover it was done in such a way that just didn't feel all that "heroic" to me.
On the other hand I had a more positive reaction to DC's New 52. I'm in a bit of minority in that I suspect so I'll explain what it was I liked vs. what I didn't like. First of all, the change in continuity, triggered by the Flash, was not something like what was done in Spider-Man - it was done to undo a dystopian timeline and the restored timeline was not as deliberate as what was done for Spider-Man. It was still most certainly an editorial decision. But I think it was one that made a certain amount of sense. In the years leading up to it I believe DC overdid it on there "crisis of the year" storylines. Moreover books like Superman and Batman had become so convoluted with their stories spread out over numerous monthly comics - it had reached the point I had long prior given up trying to read those characters. While I'm not too crazy about the undoing of the Clark Kent/Lois Lane marriage, it's worth noting that at this point I'm reading a lot more DC comics than Marvel ones at this point.
I guess in my mind my view on retcons or reboots is if the end result is good I'll likely enjoy it. I'm less crazy about changes to RPG settings. Generally speaking I prefer those that set their setting at a specific point in time and give it to the GM to do with as he or she will.