Darker than Black/WMG

The whole Gate-thing signals the series being in a Cosmic Horror universe
Given how random powers and renumerations are given, and the fact that Contractors and Dolls are stripped of their humanity, it suggests that even though the series is relatively idealistic, whatever caused the main catastrophe is really capricious.
 * The second season mentioned a prophecy from Amber involving something that would come from the Gate if "Izanami" (Yin) and "Izanagi" (Shion) ever met...

Haruhi created the Darker Than Black universe and the other SOS members (minus Kyon) are refugees from there
During an earlier point in her life (maybe the three years ago often referenced), Haruhi was having a bad day, and in an expression of her desire for a world with lots of espers, created the cataclysm of the Darker Than Black universe wherein South America was utterly destroyed and the Gate opened over Tokyo. She's Genre Savvy, so it makes sense that Tokyo Is the Center of The Universe in that world. In one episode, Haruhi makes reference to evil syndicates, which are the villain in Darker Than Black. She realized that the world she created was a dystopia, and so split it off from the real world (or else, the world of the series is a new universe), but the SOS members are from the future of the Darker Than Black world. There's good evidence that Itsuki is a Contractor. At times when he uses his powers, his body glows blue just like theirs do, and he definitely fits the personality- a perpetually cheerful Stepford Smiler prone to monologuing, not to mention that he shares November 11's quirk of following unsettling comments with I Was Just Joking. Still, through advances, he is a non-violent one. Yuki is a more advanced version of a Doll, essentially a human computer by this point. Mikuru is either a Contractor also or at least a human with those powers. In Darker Than Black, Amber can manipulate time but has the Renumeration of reverse-aging. Note that Mikuru is a time traveler and there are older and younger versions of her running around. Finally, don't forget about talking cats in both series.
 * Aha! So making other men uncomfortable around him is Itsuki's renumeration.
 * Mikuru's might be to grow moles on her body every time she travels through time. Think about it - Kyon could have easily seen the mole when Haruhi dressed her in various outfits. Presumably she gets them removed in the future, but when the older Mikuru returns she just developed one, along with her younger self.

Hei has emotions as a contractor because he didn't have any as a human
If Havoc is to be believed, Hei was "heartless" before he got his powers. That means obtaining abilities secondhand didn't prevent a personality change, and he doesn't seem to have taken on Bai's personality either. But we already know that on a hypothetical scale of Emotions vs. Stoicism, becoming a contractor drops anyone to zero. Hei was already at zero, so he dropped off the scale and wrapped back around to heightened emotions, becoming darker than black. (A caveat: I have no idea whether this is all explained in the manga.)
 * That is a really interesting theory to explain the title, but I think the implication was that Hei formerly was a monster because he was faced with having human emotions and guilt, but needing to kill a number of people to protect his sister and he's just mellowed over time. What's equally interesting is that when they show flashbacks of Amber, she's also a lot more stoic, and it seems like at that point she might not have had her powers yet. My theory, is that once you lose your morals and become a Contractor it's really easy to become Affably Evil, since there is no guilt, but since Hei didn't lose his emotions, he's stayed fairly emotionless. I also remember a comment to the effect that Contractor regain their feelings over time, and it's not clear if this is because of a Heel Face Turn or simply caused by the Gate. So, maybe because Bai is becoming more emotional inside of him, he does too.
 * Amber was already a Contractor, since she was the first Contractor.
 * Amber was the first Contractor? When did we learn that?
 * When we learned her Messieh code. Can't remember the letters, but the number was 001. They then went on to confirm that yes, she was the very first contractor.

Remuneration is an outlet for the irrational impulses built up while the Contractors' logical side is in play
Explains why Hei can experience emotion and has no remuneration, and why Wei acts in a less logical manner (as remarked on by Mao during Hei and Wei's final showdown) than most contractors: Wei is experiencing the outlet of irrational impulses even as he uses his power, due to the nature of his power/remuneration combo. Also used to explain why most contractors find their remunerations undesirable, while April, who enjoys her remuneration, drinks alcohol: alcohol already removes inhibitions on irrational impulses, so a forced outlet is redundant. The outlet is hardwired into a Contractor's brain, hence why out-of-body bodyswitchers such as Mao have "paid off" their remuneration in full. Moratorii are in a constant state of being either catatonic or chaotic because their outlet has not been formed yet. Distilled in Shihoko, whose remuneration is the return of human emotions and impulses. Maki behaved irrationally because his power, like Wei's, was actually being spent in smaller amounts in the time between laying down a charge and detonating it: likewise, his outlet for impulses was opened in a smaller form at the same time his power was spent, culminating formally in his drinking of milk.
 * ... Hei can experience emotion and has no renumeration because  As for the actual hypothesis, I have to counter with two examples in defiance: Alma's renumeration was to get older. Amber's renumeration was to get younger. These occurrences are irrational, undeniably, but they aren't exactly impulses.

Shion's power involves resurrecting Contractors
I didn't buy it given his fate at the end of the first series, but some fans have argued that. This would also explain why Hei is so intent on catching him. It also makes sense, in that Contractor Remunerations often have an ironic reflection on their powers. So, it makes sense that someone with a healing powers ends up crippled as a Remuneration.
 * Jossed. His ability is to . Hei was hunting him down on orders, and Yin is still alive.

Madame Oreille is Amber
This kind of follows from the above, and I saw on an animeblog, Random Curiosity, that several other people seemed to wonder this. First off, there two initial problems- one is that the brief times adult!Amber was shown, she was pretty modestly endowed, while Madame Oreille is the opposite. Also, I think Madame Oreille was shown at least once having blue eyes, while Amber has Eyes of Gold (although Madame Oreille wears purple glasses most of the time that obscure her eye color).

This theory for myself and others stems from Madame Oreille showing up pretty much out of nowhere to tell Suo accurately that her mother's flight would be coming in at a specific time, coupled with her general status as a Knowledge Broker who seems to know everything (being able to travel to the past and future would help with that). And, Oreille is the one who gives Kirihara a tape from Amber.

I'd also note that while a very different series, part of the reason I thought of this is because of Martian Successor Nadesico which I just finished watching and the character of Inez

Hei originally wanted to be a chef when he grew up
Because he loves food a bit too much and even if he did learn to cook just because of hunger, he's WAAAAAAAAY too good. And besides, if Bai can have a childhood dream, why not Hei?

Hei has honestly not noticed the effect he has on women
While some of it can be put down to stoicism, he doesn't act like someone who realizes that pretty much everything female and breathing falls in love with him given five minutes of conversation. Maybe Amber left him cynical, or maybe it's been happening for so much of his life that he doesn't realize those reactions aren't normal. Plus, it would be funny.
 * Or maybe he is gay.
 * Another possibility is that his effect on women is just another superpower he got from Pai. He may have realized this and learned to ignore it.
 * Well, in season 2 when Mao mentions that Suou has feelings for him, he doesn't so much as blink. He seems to notice (at least in that case), though whether he cares or not is another question all together.

This series shares a universe with Read or Die.
The renumeration of all Paper Masters is their absolute obsession with books; Nancy's renumeration is probably just wearing that outfit. are attempts at creating Contractors without any price attached. from the TV series are a prototype of memory-altering Applied Phlebotinum.
 * Wendy's ability is making really good tea. Her renumeration is being a total klutz. This is also the cause of her major level grinding; she just stopped using her power.
 * The events of Heaven's War just don't come up for whatever reason.
 * When combined with the whole Lack of Empathy thing this theory doesn't make much sense, admittedly, but considering the massive amounts of Tin Man syndrome present in the series proper...

Everything is Bai's fault.
Yes, all of it. When she was about nine, she and her brother (then around thirteen) went to watch a meteor shower out at a lake. When she saw a shooting star, she decided to combine all the things she wanted to do into one request, and went with "I wish for big brother and I to have exciting lives!" Being a little kid, she didn't realize this was a bad choice. The rest is history.
 * I can see this feeding into the Haruhi crossover WMG above...

Pai came back to life.
At the end of the second season, the star BK 201 is shown to have returned, but we don't see what happened to Hei. At first, it seems that he has to have regained his powers. Otherwise, why would the star be back? Well, it wasn't originally his star...

Hei's civilian persona (Li Shengshun) is what Hei could've been.
Think about it. Before the existence of the gates, Hei was a nice, soft spoken boy. He was much like how Li is. It's possible that subconsciously, Hei uses 'Li' because he longs for the normal life he could've had, if the gates never existed. In the season one finale,