With comics, retcons tend to go one of two ways. Either they're brilliant, and manage to reinvent an old character in a bold new way while getting rid of a bizarre story-arc, or they're just plain old bad, convoluted, and generally just quite regressive. No publisher has more experience with this old trope - arguably - than DC Comics.
The company wrote the book on retcons during the Silver Age of comics back during the 1950s, where they retired many of their Golden Age figures to different parallel Earths. Years later, Crisis on Infinite Earths would completely reset the DC Universe, cutting - ostensibly - through the chaff to deliver a more streamlined, modern mythos. Over three decades and about a dozen more retcons since, and it's fair to say the opposite effect has been achieved.
Continuity is often confusing, but for longtime fans it intimates the grandness of DC's history. Characters develop followings because of their own personalities, yes, but a lot of those personalities are informed by the various relationships and events they've experienced along the way. Take them away, and something important is invariably lost.
It's become a recurring theme over the years, so here are the times that DC's timeline tinkering caused the most amount of heartache...