Rozen Maiden/WMG

Rozen is the Millenium Earl. The Alice Game is to find a perfect CPU for his new Ark.
Both Rozen and the Millenium Earl are based off of Count de Saint Germaine or Count di Caligostro. It would be likely that the Millenium Earl is using the Rozen Maidens as his backup plan. The Maidens are obviously more complex and more powerful than the typical Akuma, so they probably have some important role in this backup plan, which the Earl initiated even as he was coming into conflict with the Black Order. The claim that the Alice Game is to find Rozen's perfect daughter is a half-truth--his perfect daughter will serve as the new CPU to his most recent Ark, a CPU loyal to only him. To keep the Exorcists from noticing, he moved the next Alice Game to Japan. There, one of the dolls, Shinku, was found by Jun. The Rosa Mystica and the Artifical Spirits are powered by Dark Matter. The cross-dimensional nature of the dolls and the Ark created the intersecting universes of the first and second manga series.

The events of the series happen in the past of the Soukou no Strain world.
See the S-Strain page for details.

Kirakishou could have been born if Enju hadn't been around.
I think Kirakishou was doomed to be forever trapped in the N field because Enju stole her incomplete body and used it to make Barasuishou's. Rozen died/disappeared soon after and the last Rosa Mystica never received a body to be installed into.
 * Very possible in the anime, but not in the manga canon, where Enju and Barasuishou don't exist.

Rozen is an alchemist
He's perfected the two holy grails of alchemy, the Water of Life making one immortal, and the homunculus Artificial Human. But is still unable to perfect the Philosopher's Stone itself which is the ultimate goal of alchemy. The Roza Mystica are actually imperfect Philosopher's Stones and the Alice Game is a system of refining the stones. The dolls can either absorb each other's Roza Mystica or refine there own into a perfect stone itself. The doll becoming a perfect girl is actually a mere side of effect of rozens true of goal creating the Philosopher's Stone, as for what Rozen has been doing all this time he has been trying different experiments to create stones but occasionally checks up on his homunculi to see if they've created a true philosophers stone.
 * This fits in with the idea that Rozen is clearly Zepia Eltnam Oberon, also known as the Night of Wallachia, who was, in fact, an alchemist.

The series actually takes place during (what else?) Instrumentality.
Except it's NOT Shinji's dream - it's Asuka's nightmare. The only male human around is a hikikomori (read: "loser") ranked only one step higher than baka-Shinji on the manliness scale. Asuka herself is invisible, imperceptible, unnoticed. And dude...homicidal dolls.
 * One could argue that Jun's getting over himself as an attempt by Lilith/Rei to keep Asuka in the nightmare instrumentality world Lotus Eater Machine style and to keep things from getting too good (Rei remembers that slap Asuka gave her prior to the second to last angel, thank you very much) horrid things start happening and get reversed with small removals of the nicer things (Hinaichigo) to keep it in a sort of balance whilst semi tormenting Asuka over it.

Also, she saw and felt, created in part by her memories of her own death in End of Eva.
 * Let's not forget that she herself could be Shinku, you know.
 * Alternately, Asuka could be Suigintou and someone else (possibly Rei) is Shinku. If Rei is mostly keeping this world intact to punish Asuka, it would make sense for her to make Asuka the broken doll who's considered "junk", the one that is obviously imperfect and doesn't stand a chance in the battles to become "a perfect girl". Perfection has been one of Asuka's driving motivations as well as self-loathing, after all.

Rozen is Enju's father
And Enju created Barasuishou to prove him that he could do better, or at least, be equal. But then, he stole Kirakishou's body, thus, making him a loser. This still sounds too much as Shinji, but hey, there are many losers out there.

Suigintoh is really really gay for shinku and wants her in the most intimate way possible
Sex? No. The rosa mystica are the dolls "souls" after all and what could be more intimate than merging with someone? This is her way of reconciling her massive gay for shinku along with her feelings of betrayal and desire to become Alice. Note that when she was destroyed at the end of season 2 while souseiseki went straight towards barasuishou(and by extension suiseiseki.) suigintoh herself made a beeline for shinku.
 * Except for one thing: The dolls were all manufactured in pairs; if you look at the main six, there are hints in their costumes that show how the pairs work; Souseiseki and Suiseiseki both have pilgrim-inspired costumes, Hinaichigo and Kanaria both have more 'childish' and frilly costumes, and Shinku and Suigintou's costumes are both a) more Victorian and b) feature a prominent rose motif. Suigintou's rosa mystica went to Shinku just because their dresses match. (Either that or even in death, she wanted to be the one to reduce Barasuishou to a fine powder, and so figured that by lending her prodigious skills to Shinku, combined with Shinku's unladylike skills at fisticuffs, would therefore win.) OR, it could be that perversely, Suigintou believed that she would be 'taking' Shinku's Rosa Mystica by merging with it. Since Suigintou appears to have the willpower of a monastary of Buddhist monks, it's highly likely that she could actually subvert Shinku's will...WHY IS THERE NO THIRD SEASON TO TEST THESE THEORIES?!!
 * The problem with that is the numbers (when they were started) don't match. Suiginto is #1, Hina-Ichigo is #2, the twins are #3 & #4, Shinku is #5, Kanaria is #6 and Barasuishou is #7. Suiseiseki and Souseiseki were the only ones made as a pair.
 * The opening to Tr Ã¤umend does show Hina Ichigo and Kanaria together, exchanging roses, right after the twins are seen touching palm to palm and embracing.
 * You've actually got Kanaria and Hinaichigo's numbers switched there, but same dif.
 * Can I thank the original poster for not taking this WMG where I thought it would go.
 * Actually, building on the OP's hypothesis: the dolls are representations of the different types of love, and they come in pairs, with the one obvious exception. Kanaria and Hinaichigo are "philos" or friendship, Suiseiseki and Souseiseki are "storge" (familial or parental love), and, yes, Shinku and Suigintou are "eros." Romantic love. Very, very gay for one another as well. As to agape, or philosophical/universal love? Kirakishou. And she was never finished. What this means is up to interpretation.

Shinku is really a MMA champion
Look at the fighting styles of all of the dolls. Every doll uses her artificial spirit as a weapon...except Shinku! She punches Suigintou. Repeatedly. And note how in her interactions with Jun, she uses her hair as a weapon. Clearly, Rozen designed Shinku to embody his secret love for mixed martial arts!

Rozen had a real daughter
We're told that the purpose for creating the Rozen Maiden is for Rozen to create the perfect daughter: Alice. The fact that Rozen even used a specific name seems to imply that Rozen really did have a daughter. In idealising her to be perfect, he could never create a living doll that matched all the aspects of her personality. At this point he either decided that he could never make a girl like Alice and gave up on the dolls, allowing them to fight amongst themselves, or succombing to defeat, decided to make the doll that fought hardest his daughter (backed up by how Rozen apparently gives Suigintou a torso). The dolls don't really become Alice - evidence points to rosa mysticae merely making dolls stronger, not changing their personalities. In fact, when Hinaichigo was living off of excess energy from Shinku, she retained her personality and Shinku didn't change at all (apart from, as aforementioned, in power).
 * Alternately, Rozen had a wife (named Alice) who died before he made the dolls, so in order to "bring her back", he decided to make a doll that was perfectly like her. He tried 7 times, but could never quite succeed. So he gave up and created the alice game to let the dolls fight amongst themselves until only one was left and could at least claim that they were Alice.

Rozen's full name is Rozen Margatroid.
Alice Margatroid is Rozen's daughter, who died, explaining her presence in what amounts to Hell. Eeh... I'll assume a fetish love for dolls runs in the bloodline.
 * Alternatively, she fell down the rabbit hole into Makai and was adopted by the local goddess. Yet she still can't replicate Rozen's crowning achievement.
 * It would make perfect sense: Rozen lost his daughter Alice, perhaps she wandered into the woods or something, when she was just a little girl, and created the Maidens as Replacement Goldfish. Only he didn't make them perfect; perhaps he couldn't, or perhaps he realized that they each needed their own imperfection in order to develop as Alice eventually would have. So they all needed to compete in a tournament named after Alice in order . Alice, meanwhile, fell "down the rabbit hole" into Makai and ended up living in Gensokyo's Forest of Magic, eventually showing doll-making skills inherited from her father.
 * Seven Rosa Mystica merge to create the Seven-Colored Puppeteer. Her new body resembles Rozen phenotypically, but her eyes change color when a different Maiden becomes the basis for her personality. This is why fanon depicts her inconsistently as a tsundere (Suiseiseki), a kuudere (Shinku), or a yandere (Suigintou).

Rozen is Akio Ohtori in disguise.
The true purpose of the Alice Game is to create a replacement for the Rose Bride should she come unruly, or a new, improved model that can fight the Swords of Humanity's Hatred, instead of just enduring their torment. Look at all the rose-motifs in the series, as well as Rozen's cold attitude towards the creations he professes to love, and how he can inspire nearly religious worship in them with most minor gestures. And besides, the little that we have seen of Rozen essentially looks like a palette-swapped Akio.

Rozen was a fan of Alice Human Sacrifice.
But since he didn't like the Vocaloids' original designs, nor the fact that there were Alice boys, he decided to make his own, and tweak the story a bit (if not a lot). And the Alice game is, somehow, a way to decide who's the badassest of all Alices. Similarities?
 * There's a red Alice (Shinku), who manages to be pretty aggressive as well.
 * There are twin Alices (Souseiseki and Suiseiseki), despite of them being blue and green instead of yellow. Their personalities match Rin and Len's Alice, with Suisei being the stubborn one, and Sousei being the smart one.
 * There's a pure madness Alice (Suigintou, sorta).
 * There are children-like Alices (Hina Ichigo and Kanaria).
 * There's a charming but rotten Alice (Kirakishou).

I couldn't define who'd be the proper singing Alice (I don't really think Kanaria could sing evil songs), but since Suigintou already filled (not really well, though) the "pure madness" side of the Diamonds' Alice, it's okay for now. And Barasuishou is a fake, so, she doesn't count.
 * There's actually a Rozen Maiden" version of Alice Human Sacrifice'' on Youtube. In it, Suigintou is Meiko (aggressive and bloodthristy knight), Hinaichigo is Kaito (singing madman), Shinku is Miku (beautiful, vain, pig-tail wearing queen) and Suiseiseki and Soseiseki are Rin and Len (the twins).

Rozen Maiden is a Christian Allegory. Rosen=God, Enju=Satan, Bara-suishou=the antichrist
It's pretty clear to me that Rozen is some type of God figure. He's immortal, not a vampire, and he's referred to as "father." Christians also refer to God as Father. Also, only God can give creatures life, this Rozen does through his Rosa Mysticas. If Rozen is/reprisents God, then Enju is/reprisents Satan. Why? According to Christian lore, Satan rebelled against God because he wanted to be supreme ruler of all. He also didn't want to bow to humanity- one of God's creations. Enju's situation paralles this. Enju does not want to admit that Rozen is the better dollmaker. (Doing so would be essentially bowing down to Rozen and his beloved dolls.) Instead, Enju decides to prove he is the better doll maker, much like Satan rebelling against his creator. He essentially makes an "anti" Rozen maiden, our friend Bara-suishou. Enju, through Bara-suishou tempts the Rozen Maidens into particpating in the Alice game, much like the Anti-Christ is said to be a vehicle for Satan to tempt humanity. Also, Bara-suishou is clearly a Rozen copy. The anti-Christ is a false copy of Jesus, ergo Bara=the Anti Christ. Yes, everybody is Jesus in purgatory and I'm sure I've just gotten on the hit list of several Rozen Maiden fans.
 * There is some serious allegorism behind the series, but it goes hand in hand with the clockwork symbology. Laplace's Demon is a concept that functions only in Newtonian clockwork universe where each component is perfectly set into place, and everything is predetermined from the start. Hence his presence in a series revolving around magical clockwork dolls. Alchemy is also present in the background, and one of the principle rules of alchemy is "as above, so below", meaning that the same patterns repeat themselves on all the levels of the universe. Hence, Rozen's and Enju's conflict's parallel to the conflict of the religious mythology above them. In this system, Rozen is basically a miniature God.

Suigintou was supposed to be Alice

 * Rozen in the beginning wanted to do a perfect girl himself. He got to the conclusion he's not capable to do it afterall. He created Rozen Maidens as he could, and left them a task, so they would improve themself. He didn't finish Suigintou, because he was making her with perection in mind he could not reach.
 * In one opening when we see the hypothetical birth of Alice from some kind of world-egg, her only clear features are long hair and wings.

Jun is either Rozen himself, Rozen's Reincarnation or his son.
Note how he is a genius dollmaker, incredibly intelligent despite spending most of his time at home doing few to nothing, seems to be capable of repairing Rozen Maiden (a task that's supposed to be neight impossible), how the Demon of Laplace (a.k.a.: Rozen's referee for the Alice Game) interacts more with him than any other character in the series and how all the dolls seem to fall for him to a certain degree, when they are actually pretty much "programmed" to strive for father's love and nothing else. (Shinku and Suiseiseki obviously have a crush on him, Hinaichigo was strongly hinted to feel the same, Canari is a little more ambigious, but also hinted, Souseiseki considers herself his Personal Slave and Kirakishou went even more Ax Crazy than she already was because of him. Suigintou... ah, she's too busy being a jerk and mourning for Megu.) In extension, the Demon of Laplace is the personification of an aspect of Rozen that Jun does not embody... kinda his "missing part".