Suzumiya Haruhi no Index

A Haruhi Suzumiya/A Certain Magical Index crossover. Aleister Crowley learns about the existence and the power of Haruhi Suzumiya and sends Touma (as an exchange student) and several other agents to test his theories about her. Meanwhile, the SOS Brigade (sans the leader) is informed of this and tries its best to not to cause any trouble and especially to prevent Touma from touching Haruhi, while the latter tries to stalk him so she can find more about Academy City. Hilarity Ensues.

First arc ended in chapter 10, second arc ended at chapter 18. Last updated in 2013 with chapter 24 (in the third arc). Needs More Love, indeed.

Check it out at FanFiction.net.

Tropes used in Suzumiya Haruhi no Index include:

Big Eater: Index, just as much in the original material if not more, at one point she eats so much free ramen she actually manages to make the stand bankrupt and it's owner cry.
Brick Joke: Haruhi reads a paper on stem cell research and becomes interested. Several chapters later, Heaven Canceller out of nowhere declares he will work on stem cell research, and Kyon deduces that Haruhi's power caused this.
Broke Episode: In chapter 13, the brigade has to work in the family restaurant they always go to so they can help Kyon pay for his trip to Academy City.
Erotic Dream: Kyon has one about both Mugino and Asakura.
Eviler Than Thou: Asakura Ryoko Vs. Vento of the Front. The segment where this fight happens was even named after this trope.
Fastball Special: Emiri Kimidori flings Touma into the sky so he can punch a flying Kakine.
Finger-Poke of Doom: Haruhi is able to bypass Accelerator's powers and flick him in the nose.
For Science!: Crowley doesn't care that negating Haruhi's power or otherwise messing with her could potentially destroy the universe, he's curious.
God Guise: The magicians worship Haruhi behind her back, believing her to be The One True God, except for the Roman Catholic Church, who think she's a heretic who stole God's power. Then in the third arc, it's revealed that the Roman Catholic Church believes it's Sasaki who's The One True God.
Idol Singer: Haruhi becomes the talk of Academy City after an impromptu performance. She does have the voice of God, after all.
Rescue Romance: When Kyon rescues Mugino, she instantly ~~crushes~~ lusts after him, much to his ~~annoyance~~ horror.
Schrödinger's Cat: Thanks to Haruhi's subconscious Reality Warper powers, when asked to guess a card randomly drawn from a deck, she can guess a card that isn't in the deck and get it right. Some observers describe this as if someone did the Schrödinger's Cat experiment... and pulled a dog out of the box.
Shout-Out:

Saten: "So Haruhi san, tell me which side of a chocolate cornet do you eat first?"

Mugino: "Mugi chan she says… what am I some kind of moeblob now? My eyebrows are perfect damn it!"

Haruhi: "You know what they say Capitalism, Ho!"

- When in the closed space that formed when Touma touched Haruhi, Kyon says that Kanzaki and Nagato carved "a weird circle that looked like something out of that alchemist manga that ended recently."
- The scene where Index was visiting Touma in the hospital while eating melon bread, and eventually offering one to Touma reminds one of a certain blazing Tsundere.
Surveillance as the Plot Demands: Aleister Crowley is able to see nearly anywhere, even inside Closed Space. Lampshaded by Motoharu.

"Mind if I ask something… how did you saw all that stuff?"

Time Stands Still: When Touma touches Haruhi with Imagine Breaker, this happens as Closed Space/the universe starts being negated/erased. Fortunately, the people who were unaffected manage to separate them before it is too late.
- Nagato uses the power to freeze time to effortlessly defeat Accelerator.
The Un-Reveal: Once the SOS Brigade realizes that Touma is not affected by Haruhi's powers, they excitedly ask him what happened in the Time Crash Three Years Ago. Touma sadly informs them about his amnesia.
Unwanted Harem: Touma, just like, if not more than, in the original; by now, he (of course unintentionally) charmed one-tenth of entire female population of North High.
Wham! Episode: Chapter 11. The SOS Brigade gets invited to Academy City.
Wham! Line: You know the first line Haruhi spoke in the original source? She says it again...IN ACADEMY CITY!!
- In Chapter 18, Aleister receives a phone call: "My name is John Smith."
What the Hell, Hero?: Tsuchimakaido receives this from nearly everyone else for telling Aleister about Haruhi in the first place just so he could have a bargaining chip to legalize marriage between Not Blood Siblings. Hell, even Aleister calls him on it.

Aleister: I refuse to take morals lessons from someone that sold off his God just because he wanted to marry his sister.

Who Writes This Crap?: Haruhi asks who thought Touma and her touching each other being big deal was a good idea for a plot and says it's ridiculous, referring to what she thought was a play the brigade had done for her.
Yandere: Hilariously enough, Mugino becomes one for Kyon.