Haruhi Suzumiya/Tsuruya/WMG

Tsuruya is a different "Writer God", who doesn't interfere with Kyon and Haruhi.
In the novels, Itsuki comments that she's very mysterious; it's possible she's running around having her own adventures with fantastic beings different, separate from the groups that Kyon is involved in. She herself comments that she's a "Cameo Appearance" in the movie that Kyon and Haruhi made; all of the elements within turned out to be real in a fashion. In the novels, she has joked that the Masquerade that Kyon's explanations provide isn't particularly effective, but also, that she's not going to get involved besides being a very amused spectator. Kyon never acknowledges her saying this.
 * It would seem Tsuruya's adventures (based on an off-hand comment) involve Espers, Aliens, and Precursors with super-advanced technology. She "shares" the Aliens and Espers with Haruhi. Note the interesting discrepancy, in the Kyon/Haruhi verse, the Precursor Technology concept would completely conflict with their current "definitions." Therefore, she avoids direct interaction in order to prevent an Armed with Canon situation (between gods) that could damage reality. Kyon's willful rebellion to the Time Travelers in unearthing the Out Of Place Artifact could have significant results metaphysically.
 * Alternatively, Tsuruya is in fact Sounds like a character created specifically with Armed with Canon in mind, don't it?

Tsuruya is a Mad Scientist, or at least the daughter of one.
Well, we already have a regular powerless character. Mad scientists tend to maniacally laugh at any time, and also Tsuruya has a connection with Asahina. While it's probably true that she's not from Mikuru's time (She said so herself, although she might be lying) her tendencies could have attracted her to Mikuru. Plus, Time Travellers and Espers in this show are not super obvious, so why would Mad Scientists be any different? Or maybe...
 * Plus, she's got a pretty big house, so she's probably rich. Also, her family DOES have ties to the Organization, perhaps providing them with technological support. It would also explain the

Tsuruya is a Vampire
And since she's immortal, Mikuru knew her in the future. That stuff about vampires dying in the sun is crap anyway.
 * And after all, she appears to be undead in the movie. If the cat can talk because of Haruhi, then how do we know Tsuruya, Taniguchi and/or Kinikida weren't changed also?
 * And the obvious quality...

Tsuruya is a devil, or the Slider herself. Heck, she might be God!
It wouldn't make sense on how she is a normal person besides Kyon in the SOS Brigade. Also, she has alternate adventures of her own, indicating that she might know how to work on different dimensions, and maybe she's hiding her powers to not cause a dimensional collapse (or maybe she doesn't even know that she has such powers). She could be the devil that Haruhi searches for because her general appearance reminds of a demon girl, and just because she laughs too much at the most meaningless things, like a trickster devil. Maybe all the plot is a plan by her, to make people think that Haruhi is God.

There are no sliders because Kyon hasn't met them yet
Specifically, because he hadn't met them yet in book two, when he went back in time. While talking to Haruhi, she asks if he thinks Aliens, Time Travellers, and ESPers exist, and he says yes to each. She then asks about Sliders, and he replies "I haven't met any yet". Since this was more or less the point when Haruhi recreated the universe, there being no sliders is actually part of a Stable Time Loop in itself. For a slider to come into existence, Haruhi will need to recreate the whole universe again, or at least create a separate universe that they can slide from

Tsuruya is immune to all forms of mind control
The characters in the "Adventures of Mikuru Asahina" are all similar to their actors. When Yuki brainwashes Tsuruya and the other two, Tsuruya's dialogue clearly shows that she is only pretending the be controlled and thus the real Tsuruya must be immune to mind control.

Tsuruya is God
And she has put Haruhi in control for the lulz. It worked.

Tsuruya is completely normal
...and created by Haruhi, most likely subconsciously. She was given all sorts of odd qualities and has an unusual sense about her to make Kyon wonder about her. Tsuruya was made to be the mystery that no one could solve.

Tsuruya is a time traveller.
And also, one of Mikuru's superiors. As shown in The Sigh of Haruhi Suzumiya, or the anime at least, Tsuruya shares the same ignorance towards modern technology ("Is this what video cameras are like there days?"). Also, in the novels, Tsuruya knows quite a bit more about the SOS Brigade than it appears.

Tsuruya is older than she might look.
Taking in consideration the example above ("Is this what video cameras are like these days?"), Tsuruya could actually not been from the future, but, in reality, she could not have updated herself technologically-wise, and may still be in an 80's mindset. If she's 40, 400, or 4000 years old, it's up to the reader. The reason could be either because she's a demon, or because she's plainly an extremely advanced robot, like Maria.
 * This fits in nicely with the above Vampire WMG.
 * Totally agree! This occurred to me about Tsuruya as well. She continually acts like long-lived character types you see in other animes, movies and television shows. The "is that what [they] look like these days?!?" is only one example. She's confident, raucous, behaving almost like Doctor Who in a new time zone just living it up like a tourist. If Tsuruya is not a vampire, then she is some sort of immortal (Highlander anyone?), long-lived creature taking human form (dragon?), or spirit taking on human form. Since its a Japanese show, she might even be akin to the Kitsune who can take human form (although they usually have some strange physical trait that remains like... cute little fangs!)

Tsuruya is the slider
Because someone has to be, and we all know that Tsuruya is hiding some sort of secret.

Tsuruya has a physically identical twin.
Haruhi knows that every show will at some point have a reason for twins and as such made the universe prepared, with an identical copy of Tsuruya who acts far more mature than her sibling. Because everyone's on a Last-Name Basis with Tsuruya, no-one can tell the difference until they're both in one place. Since Kyon's only had one serious discussion with Tsuruya, he's only met the serious twin once.
 * Now I have this mental image of Tsuruya as Alpharius

Tsuruya is a
How has this not been suggested yet?

Tsuruya is like Kyon, whatever he is.
Technically this needn't disprove her being a Slider. Kyon's "slid" enough through dimensions despite seeming to be the normal one of the SoS Brigade. Technically, all of those times were effectively against his will originally.

Tsuruya is mysterious and has her own goals and background. She apparently knows enough to repeatedly as of volume 7 to tell Kyon "We're the same thing. Not like them". Borrowing from above, Tsuruya in the movie states she is only pretending to he mind controlled. What character has been practically immune to every dimension rewrite or noticed odd things? Kyon. Tsuruya's role balloons greatly in the same novel we are introduced to the anti-Mikuru, anti-Koizumi and the story after we see the first hints of the anti-Nagato.

This doesn't mean she is the Anti-SoS Kyon. She could be a rival Writer God to Kyon's True God WMG. If Kyon is a reality anchor, Tsuruya could be another who is aware enough of her nature to attempt to remain untethered to Haruhi.

Tsuruya is a government agent
Tsuruya is working for the Defence Intelligence Office DIO [Jouhou Honbu] or the National Police Agency [NPA - Keisatsuchi] in a sort of "X-Files" role. The Japanese special intelligence services long ago detected anomalies occurring at North High and around Haruhi Suzumiya and inserted Tsuruya as an agent to find out what is going on. As there is nothing really "weird" about Tsuruya, other than being a government agent, Haruhi did not subconsciously drag her into the SOS Brigade - although Haruhi tolerates her as an "associate member."

In this guise, Tsuruya is probably older than a High School student but just has a younger appearance. This makes a lot more sense than her being so fabulously wealthy. She is supposed to be so wealthy that her family owns numerous houses and even numerous ski resorts. There is no way that an heiress with such a background is going to be attending a broken down prefectural school! An heiress of this level would be in Eaton or something.

On the other hand, as a government agent, Tsuruya would have access to facilities to bring the SOS Brigade to for observation and study under the guise of having her family "own" them. Another giveaway is the skillful and police-like questioning Tsuruya often subjects Kyon to. She's trying to play the "good cop" and claim not to really care what is going on as long as Kyon takes care of Mikuru. However, she skillfully questions Kyon to let him know that she knows good and well what is going on then backs off, trying to draw him out. Tsuruya being an undercover agent would also explain her combat training abilities (alluded to in the movie and shown to humorous excess in the Haruhi Suzumiya-chan spinoff cartoons).

Tsuruya is a manifestation of Haruhi's subconcious.
In the same way that Yasumi was created to save the brigade from that particular crisis, Tsuruya in there for a more permanent kind of support. It has been stated that the Tsuruya family is strongly linked to Koizumi's Organization, wich in turn provide for a lot of the Brigade's adventures. She protects and gives moral support to Mikuru, so Haruhi doesn't feel guilty about abusing her. She blatantly flirts with Kyon so as to express Haruhi's feelings, but never seriously because Heruhi wants him for herself. Koizumi mentions that Tsuruya may be having her own adventures offstage, wich would satisfy Haruhi's fancy for great adventure without cutting into the brigade's time. The similitude between them is explicitly and frecuently metioned. She supports all that Haruhi does, but stays out of the limelight because Haruhi has given her a secondary role (She didn't even want Yasumi to join, but she was forced to allow her in because it was part of the mission to save her friends). Tsuruya is also a filthy rich genius that could go to the best schools in the world and yet attends a crappy prefecture high. Kunikida admits that he only went to north High to meet Tsurya and he was the only friend of Kyon's in high school before the Brigade, thetefore Haruhi broght him to keep Kyon company. As Haruhi comes closer to coming to terms with herself and her power, Tsuruya starts having a more explicit role, providing the treasure map and the cabin for the Sonwy Mountain Syndrome so they can have fun and becoming closer to all the gang, but always staying in the sidelines and refraining to question anything, since tht's not the job Haruhi gave her.