Haruhi Suzumiya/Itsuki Koizumi/WMG

Itsuki is really God
This is mostly based on how the "Kyon is God" theory has the problem of Kyon not saying he is, while there are the many problems with accepting "Haruhi is God" that the "Kyon is God" theorists have highlighted. In this case, the entire situation would be conducted by Itsuki for his own amusement; he prefers to stay on the sidelines and watch the love story that he has constructed for himself unfold, and probably take a Third Option Love Interest for himself at the end. It is very likely that if this were true, Haruhi is in fact within the loop of aliens, time travelers, and espers and has been told that Kyon is God. The main problem with this theory is that it would lack the narrative coherence of Kyon or Haruhi being God.
 * I'd have to say (in response to all the "X is a god" ideas really: Define the nature of god. We tend to assume that the god that one or other of the characters is is God in the abrahamic sense of the word, I.E an all powerful being, however there are many differant interpretations regarding the nature of "god" wherever you look. So who's to say that a being with the power to do some of the stuff that happens in the series is really a god?
 * You've made a good point. By one definition, anyone or anything that is worshiped by a person can be considered a "god," regardless of if that "god" has any actual power.

The entire series is a Batman Gambit on the part of Itsuki, who not only is aware of the Fourth Wall but is also the true "God" of the show.
Itsuki harbors a crush on Kyon; however, being aware of their existence as a fictional property, he knows that making the Ho Yay too obvious actually results in a lesser amount of fanwork. So he creates a cast to deflect most of the criticism from hetero guys with Moe Moe archetypes, while making the Tsundere female lead juuuuuuust unlikable enough so that anyone with yaoi tendencies will find her unsuited for Kyon. Thus, the amount of Itsuki/Kyon grows, encouraging the production of more fanwork, and allowing more hints to be dropped in the anime/novels/show itself, thus resulting in all those scenes where Itsuki gets to make Kyon uncomfortable. Supported by Itsuki's lame excuse that he's only doing it to ward off Haruhi's attention, as all the moments where he's expressing his fondness for Kyon take place away from Haruhi's eyes.
 * ... This makes too much sense to me. Oh Haruhi.

Alternate alternative: Itsuki is the slider, and Kyon is the esper
Itsuki has dimension jumping powers. In fact, his power to identify Haruhi's emotions could easily be related to the ability to see into Closed Space, and he could transform by moving himself slightly "out of phase" with the dimension he's in. Thus, all of Itsuki's powers are related to alternate dimensions and "esper" was just the label Kyon attached to him. Slider would be a better description of his powers.

Espers are lying about only having active powers in Closed Space
Which could explain the above non-Haruhi instances, this would also mean that Kyon's supposedly Muggle friends are Espers. He does ask one if they're "special" and gets a laughing response that he's been infected by Haruhi. What Kyon doesn't get is a direct answer.
 * They don't have to be Itsuki's brand of espers. They could have some other sort of ESP, even unknowingly. Like Nakagawa (below).
 * How was Itsuki and his organization able to investigate Kyon and determine that he was completely ordinary? Turning into balls of light inside a closed space doesn't really lend itself easily to that sort of thing...
 * Itsuki (or someone in his organization) was also able to perceive something about Nakagawa's powerâ€”that Nakagawa had it, if nothing else. Nakagawa was the kid who was unknowingly able to catch glimpses of the Integrated Data Entity through Nagato, something that Itsuki presumably cannot. With regards to the kid, Itsuki says, "To be honest, you sure do have a lot of extraordinary friends." Now how many friends does Kyon really have?
 * Let me reverse this. They only have active powers inside closed spaces. Their passive powers allow them to see the interfaces, track closed spaces and read thoughts or at least feelings, but they can't zap people with red balls of light without first having somebody else suspend the laws of physics for them.

Itsuki is being Ambiguously Gay in the way he is as two different backup plans.
Plan 1: In the event that Haruhi is a Yaoi Fangirl: Get Kyon used to the idea of being with Itsuki, to keep Haruhi entertained if she gets bored with Mikuru. (This works if Itsuki really does like Kyon, because he can say it's not just because of Haruhi when and if they have to placate her.) Plan 2: In the event that Haruhi wants Kyon: Back off and let her have him. If Haruhi doesn't think Itsuki's competition, he won't be eradicated. Secondary reasons may also exist (regardless of attraction) depending on how much Itsuki really knows. For example, if Mikuru falls for Kyon (or Itsuki) and Haruhi has shown attention for him, they can pretend not to be interested in girls while Haruhi isn't there without letting Mikuru know about Itsuki or Haruhi's powers. Related, if Kyon gets caught "flirting" with Mikuru like in the anachronic finale, he and Itsuki can improvise the same thing without making Itsiki's cues obvious to Haruhi, and later add If It's Haruhi It's Okay to Kyon's act if she is being posessive of him and not of Mikuru.
 * however he could be doing this since haruhi thinks of him as gay, and he may love her, which would explains why he's always trying to please her

Itsuki really does have a girlfriend/boyfriend.
In volume 9 Kyon asks if Itsuki has one. Itsuki "gives a bitter smile". Kyon goes on to think, "Even if this guy has a girlfriend behind my back, it wouldn't be surprising at all". In volume 4 Haruhi asks, "Koizumi, are you going to be on a date with your girlfriend?" to which the guy in question denies. The guess here is that he places the activities of the SOS Brigade and the Organization above a relationship; however, having a relationship in high school fulfills part of his "want to become someone who appears to be a normal high school student." It either might be a sincere relationship or superficial (think: appears to be).

Itsuki Koizumi is the son of Japan's former Prime Minister Junichiro Koizumi
And Itsuki's hair will grow to be as grand as Junichiro's.
 * Jossed, Itsuki's family name is written with the kanji 古泉 (old spring), the ex-Prime Minister's with 小泉 (small spring).

Itsuki's Gratuitous English line in "Endless Eight"...
Will be translated into Japanese in the dub. The dub writer will do the same thing he did with the "Naze? Why?" scene and make Johnny Yong Bosch say "" instead of "".
 * Personally, I think it'd be funnier if it was translated as ""...
 * And this one thinks if would be funnier still if it was changed to "Voulez-vous coucher avec moi ce soir?"
 * Jossed. He simply puts an emphasis on "I love you".

Itsuki is the Big Bad.
He is, in fact, the LEADER of The Organization. As far as we seen, he tends to be.....unreliable when it comes to talking. Maybe he wants to get rid of/hijack Haruhi's power. Or maybe he's just there for some lulz, sort of like Gin Ichimaru.

Itsuki is wrong: Haruhi wouldn't magically retcon him into being gay for Kyon... because she already did.
As noted by many a fan, the majority of Itsuki's Ambiguously Gay behavior occurs when Haruhi isn't looking - just like all the supernatural occurrences. The one time when Itsuki admitted having a straight crush on Haruhi? In Yuki's retconned world where Haruhi had no reality-warping powers. Whether Itsuki isn't aware of this or does but is simply too embarrassed to admit it is still up in the air.
 * Is the above troper talking about the line "Don't you think it's about time that I take off this harmless looking mask and change this image that I don't even know when I created it for myself?" or "My present image fits perfectly with how Suzumiya-san would imagine me to be"?
 * In either case this WMG means that Itsuki didn't have a choice in becoming gay; he was forced to. (Homosexuality linked to DNA excluded here.)

Itsuki is an Artificial Human created by the organization.

 * It came to me when he mentioned Omphalos Theory (he's a freshly created Artificial Human with all those Fake Memories planted in his brain) and said that his real personality is less than pleasant (he doesn't have a real one); it always felt as something of a Foreshadowing to me. So maybe how he told Kyon in sixth novel that he will to help Kyon is the former going through similar characterization of Yuki.

Itsuki is constantly testing Kyon by....
...playing the board games. Those games he plays with Kyon are actually something of a disguised aptitude test, trying to investigate him further.

Itsuki did not exist three (or four) years ago and is not aware of the fact.
He hints that he is interested in time traveling, even if he "can’t see the past me". The reason Mikuru won't let him tag along (in addition to (1) Kyon finding him annoying and (2) a third traveler being completely pointless) is that as a time traveler, she knows that he doesn't exist. To reveal that wouldn't be good. The only grounds for this is that in all the time traveling arcs, we see past Yuki and past Haruhi. The only one we did not see is past Itsuki.

Itsuki is a Troll.

 * Doesn't it make sense?

Itsuki was given his powers by the IDSE.

 * Note that Itsuki had some of his powers in a space created not by Haruhi, but rather by a data-vore.
 * The IDSE pointed the espers at Haruhi to cover their tracks WRT Kyon. (He just knows his connection to Haruhi.)
 * The IDSE uses the espers to help cover for their poor interfaces. (Being natives they blend in better.)

Itsuki's compliments have backfired.
Haruhi is unable to accept compliments and so Itsuki's use of them drives her away into the arms of Kyon whose internal snarking seems more like the kind of silent support Haruhi seeks.

Itsuki has already told us that he is a time traveler.

 * "If I am born there" is another throwaway fridge-logic line. Why should he assume that he's likely to be born into a world that only has Haruhi and Kyon?
 * Therefore he really likes his parents and wants them to get along, but has no tolerance for dad hitting mom.

The baseball tale was a fail for Itsuki's evil plan.
On the way back from Apartment 505, Haruhi is leading Kyon somewhere and then Kyon stops her by being a jerk. (They were going to the wrong side of the tracks from either of their homes.) When Kyon returns home he finds Itsuki is surprised to see him back so soon. My suspicion is that Itsuki planted some super-romantic thing on Haruhi and was foiled by Kyon's blockheadness.
 * "Ah, Miss Suzumiya, I've got these tickets for this play/movie/dinner tonight, but my part time job just called. So rather than letting them go to waste, I'll just leave them with you. Thanks."

Nagato is Koizumi's mother.
Blame Haruhi for this one.

Itsuki is Kyon
Maybe a Literal Split Personality thing, maybe something else, but Kyon's introduction did involve him saying he had wished to be an Esper,then decided he'd be better as the Esper's sidekick who didn't have to do all the work.

Itsuki was originally going to be the slider.
Word of God says that Kyon was originally going to be an esper, if that is the case than what was Itsuki going to be? A second esper? I think not! The whole sliders thing that Haruhi mentions is just something that Tanigawa forgot to write out of the story, because Itsuki was the slider during early writing.