In The Sandman graphics novels, frequent mention is made that Delirium of the Endless (her siblings are Destiny, Death, Desire, Despair, Destruction, and Dream or Sandman) was once Delight. But I cannot recall ever learning how the change came about.
Is it merely a psychological fact of maturity projected into the medium?
Or is there a mythological basis for this souring of Samadhi, so to speak?
In-universe, Delirium is most easily interpreted as an abuse victim. But both Dream and Delirium appear to be built on a template from Freudian psychology, which out-of-universe helps explain Delirium's change.
There's a Gaiman-sanctioned but unpublished story by Karawynn Long which points in the direction of Delirium having been mistreated. As Christi mentions, there's also hints in the canon that it was a broken love affair (The Destruction story in Endless Nights) or even a violent rape. As pointed out by others, Delirium's aversion to being touched would match someone being repeatedly raped in a destructive relationship. A flashback in one of the Sandman stories shows Delirium meeting with Destruction when she is gradually changing from Delight to Delirium. Destruction is clad in fur, indicating that the change took place in prehistoric times. This excludes modern drug abuse as the cause. (In contrast, Destruction's departure is clearly linked to another defining 20th century phenomena)
Delirium: What's the name of the word for the precise moment when you realize that you've actually forgotten how it felt to make love to somebody you really liked a long time ago?
Dream: There isn't one.
Delirium: Oh. I thought maybe there was.
Delirium and Dream, in The Sandman #43: "Brief Lives: 3"
Not knowing everything is all that makes it OK, sometimes...
The Absolute Sandman, Vol. 1
Importantly, Long connects Delirium not only to the mistreatment but also to putting a lid on it and refusing to acknowledge it to oneself. This nicely matches a theme in the finale of The Dreaming story arc, where a mistreated individual combines with a fact that Dream tries to hide for "himself" and creates a schism in the dreaming itself.
I believe that both Long and Gaiman are highly influenced by Freudian psychology, which explain a lot of mental illnesses as due to suppression of either memories or desires. This also fits with Desire's involvement in the schism and Dream in the final issue of The Dreaming coming to terms with Desire in some unspecified way, after having been antagonistic to her ever since the storyline in Endless Nights. In Freudian terms he has stopped suppressing.
However, Gaiman has also played on the old theme of too much knowledge causing madness. Specifically this quote:
Do you know why I stopped being Delight, my brother? I do. There are things not in your book. There are paths outside this garden.
The Sandman, Vol. 7: Brief Lives*
In the Destruction story in Endless Nights, Delirium makes a second reference to this, which can be interpreted as a multiverse reference. But maybe Gaiman intends to say that one can go mad dwelling on what could have been?
Gaiman presents a synthesis in Morpheus funeral, where Destiny speaks of him representing what is, Dream representing what is not and will not be, but providing a fresh point of view of what is. Note that this is Destiny's first appearance after he himself had an unsettling brush with the multiverse. I think Gaiman's theme here is one of maturation. Accepting that you have been shaped by previous events in positive and negative ways, not suppressing your subconscious and accepting that when you open one door you close another in your life.
You can see the same theme in Dream and Delirium's search for Destruction. In their meeting with Destiny (what has been and is) Dream is forced to face a suppressed memory of his son and it is Delirium, who has faced hardship before, who is the only one strong enough to keep their act together. It is probably not a coincidence that dream's son Orpheus represents Catharsis, the cleansing purging of emotions. Recall that his song could make even the Fates (the Kindly Ones) cry. It is very fitting that Dream and Delirium, after first facing the facts of the past (Destiny) then goes on to visit Catharsis (Orpheus) and only then succeed in reaching change (Destruction). I won't say that The Sandman stories are veiled summaries of Freudian therapy sessions, but the overarching storyline is certainly one of personal growth and maturation.
To the best of my knowledge, it is never explained in any in universe material, although some have suggested the trauma of a broken engagement, based on the fact that Delirium mentioned in "Fables and Reflections" that she was engaged once, and Destruction speculates in "Endless Nights" that someone may have broken her heart. There is very little evidence to support this, however.
Delight is in some sense an avatar of innocence, and I suggest that the transformation occurred because she, or the universe, or both, lost their innocence, and the only way that an innocent could cope with the world after this was to embrace madness. The alternative would have been to die, which is the option Dream chooses when faced with a similar need to change his own essential nature.
There will be a lot of pictures here.
One other overarching theme in The Sandman is responsibility. Dream takes his responsibilities very seriously, but he knows there's more to it - namely the fact that he, and the other Endless, are shaped by them.
In a panel from the epilogue of The Doll's House, Dream tells to Desire that it is the Endless who are puppets of the living beings, not the other way around. After Dream leaves, Desire refuses to believe that, and provides interesting insight into the thought processes of the Endless:
Here and afterwards, all pictures are clickable to see the full-resolution version.
The realisation of the fact that the Endless are merely servants appears to be hard for them. For one thing, Destruction did abandon his realm, precisely because he realised the Endless, as the embodiments of their respective areas of influence, are not needed at all - the Universe can do as well without them.
Brief Lives, chapter 8: "Journey's End".
Destruction, and creation, is still occurring - only Destruction is not responsible for it:
Ibid.
When Dream was imprisoned in Preludes and Nocturnes, people still kept on sleeping and dreaming (although there was a short period of encephalitis lethargica, and The Dreaming had decayed as well):
The Sandman #1 - "Sleep of the Just".
Going back to Delirium, she seems to know very well why she changed from Delight:
Brief Lives, chapter 7.
She practically confirms the things Destruction later says about the Endless and their responsibilities.
The paths outside of Destiny's garden are not elaborated on in the main series, but we get an idea about them in The Sandman: Overture:
The Sandman - Overture #5
This ship was created by the dreamers, in a desperate attempt to flee the destruction of the universe. It was not originally a part of this universe - and in the end of Overture, when the universe was permanently overwritten, it was shaped by the dreams of the passengers of that ship. This part is similar to "The Dream of a Thousand Cats", which is also mentioned in Thaddeus' answer:
Dream Country, "The Dream of a Thousand Cats" (issue #18)
No one, even the Endless (except only Dream), remembered anything from the previous universe, because it never even existed:
The Sandman - Overture #6
So the dreamers, and by implication - all leaving beings - have power over even Endless, and Desire was not happy at all about it. I'm not quite sure why Delight was affected so drastically by this revelation, but there's a bit of information from The Sandman Companion, where Hy Bender and Neil Gaiman discuss the origins of the Endless:
NG: I decided Delight would would make for a very appropriate past existence for Delirium, because she's a character I wanted in a state of flux - she's been one thing, she's become something else, and eventually she'll change into something else again.
HB: Is this state of flux unique to Delirium?
NG: Yes. It has to do with her being the youngest; she's practically a cosmic afterthought.
The Sandman Companion, chapter 13 "Secret Origin", page 241 (first edition).
Purely for comparison, this is true even for Death - Hob Gadling, for instance, will not die because he doesn't want to; this is another example of an Endless being dependent on the will of their subjects.
Doll's House, "Men of Good Fortune".
There is another side to this - Delirium realises she is subject to the will of living beings, yes, but she also knows that she affects their lives as well, even indirectly:
The Kindly Ones
And she also says that her and Destruction's mere presence caused a wibbly-wobbly ball of reality alteration in "On the Peninsula", the Destruction story from Endless Nights:
Though Delirium doesn't usually show it, occasionally her wisdom pours out, and proves that she knows at least as much as her siblings, if not more:
Left - Season of Mists chapter 1; right - The Kindly Ones.
I conclude that a combination of factors caused her to be changed from Delight to Delirium:
Her age makes her unique among the Endless, always in a state of change.
Despite her age, she is very wise, but it looks like in her case the wisdom came at a price - staying in the "serious" state causes her pain, so most of the time, it's easier for her to be a bit crazy, and sometimes fish.
While I can't provide more insight to the question "Why" - previous answers provide enough information pointing it to some traumatic experience, i.e. lost love, as suggested in "The song of Orpheus":
I'd like to point more to the "When": it had to happen much earlier than some answers suggest, when Morpheus was imprisoned by gods attempting to takeover the dream, he attempts to get help from Delight but she refuses because "she is changing"
With help of Desire Morpheus kills the gods and turns skull of one into his helm, that since becomes his sigil.
It is said that even destiny doesnt know why delight changed her identity. The comics say that the reason is only known to Delirium herself. But i really like the "universe losing innocence" suggestion put forward by Christi. Like they say, sometimes when you fall, you fly. :)
Delight turned to Delirium, because ignorance is bliss. As time went on, the more knowledge she gained, changing her to Delirium.
While Destruction is seen wearing furs this does NOT isolate him to Pre-historic times as previously suggested, but also the 1700-1800's. Destruction is already discontented with the ways that the natives of America were being destroyed, and the wilderness being plundered to fuel the revolution he sees as most vile, as Destruction is now meaningless to Mankind. It's too easy for them to do, and too easy for them to rebuild and try and forget the madness that once possessed them, therefore allowing it too easily to happen again. He confesses that he is tired, as this new pace is entirely too much for him to deal with. We see him visit Delight during this Endless Night story; she is dressed in regency period clothing. This is also the time frame where Mankind delved into developing drugs, such as opium, heroin, and morphine. This would mean that Desire had raped Delight, and transformed her into Delirium. How can we see this to be true? If it were a simple matter of Delirium just changing, her other siblings would attempt to 'comfort' her as they do Dream during the dinner party/family meeting. If someone else had acted as a harmful party to one of the Endless, they would gather and destroy said entity, as that would be akin to change Destiny's course, Death's abilities, etc. You would think if Desire cared for their sister, that at least they would show up, even if it was a back handed attempt at manipulating Delight. Unless they were responsible.
But, none of the other siblings attempted to comfort her, which implies it's one of their own, and they don't want to take sides: Dream by this time was lost(a concoction of Desire and Lovecraft-esque plotting), and both Destiny and Death don't give Desire or any of their actions the time of day. Despair would only add to her sister's punishment, and doesn't care for Delight/Delirium as she provides an escape for Despair's victims.
Only Destruction provides comfort to Delight, and thereby aids in the destruction of Delight to enable her to embrace her new identity as Delirium.
For the 'psychological' camp, I found this, from Jung's Psychology of Kundalini Yoga.
For the convictions of the muladhara world are very necessary. It is exceedingly important that you are rational, that you believe in the definiteness of the world, that this world is the culmination of history, the most desireable thing. Such a conviction is absolutely vital. Otherwise you remain detached from the muladhara--you never get there, you are never born, even. There are plenty of people who are not yet born. They seem to be all here, they walk about--but as a matter of fact, they are not yet born, because they are behind a glass wall, they are in the womb. They are in the world only on parole, and are soon to be returned to the pleroma where they started originally. They have not formed a connection with this world; they are suspended in the air; they are neurotic, living the provisional life. They say: "I am now living on such-and-such a condition. If my parents behave according to my wishes, I stay. But if it should happen that they do something I don't like, I pop off." You see, that is the provisional life, a conditioned life, the life of somebody who is still connected by an umbilical cord as thick as a ship's rope to the pleroma, the archetypal world of splendor. Now, it is most important that you should be born; you ought to come into this world--otherwise you cannot realize the self, and the purpose of this world has been missed. Then you must simply be thrown back into the melting pot and be born again.
The Hindus have an extremely interesting theory about that. I am not strong on metaphysics, but I must admit that in metaphysics there is a great deal of psychology. You see, it is utterly important that one should be in this world, that one really fulfills one's entelechia, the germ of life which one is. Otherwise you can never start Kundalini; you can never detach. You simply are thrown back, and nothing has happened; it is an absolutely valueless experience. You must believe in this world, make roots, do the best you can, even if you have to believe in the most absurd things--to believe, for instance, that this world is very definite, that it matters absolutely whether such-and-such a treaty is made or not. It may be completely futile, but you have to believe in it, have to make it almost a religious conviction, merely for the purpose of putting your signature under the treaty, so that trace is left of you. For you should leave some trace in this world which notifies that you have been here, that something has happened. If nothing happens of this kind you have not realized yourself; the germ of life has fallen, say, into a thick layer of air that kept it suspended. It never touched the ground, and so never could produce the plant. But if you touch the reality in which you live, and stay for several decades if you leave your trace, then the impersonal process can begin. You see, the shoot must come out of the ground, and if the personal spark has never gotten into the ground, nothing will come out of it; no linga or Kundalini will be there, because you are still staying in the infinity that was before. (italics original, bold mine.)
I suppose what this answer amounts to is that it may simply be Neil Gaiman's genius to capture this fact in poetry.
