My favourite Halo concept (and stories that deal with it) is regarding the Artificial Intelligence construct. We see numerous perspectives of "life" in the Halo universe - human, alien (Covenant), 'dead' (Flood), 'kin' (Forerunner), artificial (various types of advanced AIs). All of these wound together, when dealing with the nature of Life and survival, make me love stories that attempt to touch on this topic...
Which of course brings me to
I love bees!
;)

It's not so much a classic "Halo" story, since it's more a character drama, not a lot of military action, and only vaguely references explicitly Halo content, but the story showed that the Halo universe is dynamic, able to contain a wide variety of stories and genres, that there's really no excuse for the Haloverse itself to grow stale. Bad stories, ultimately, are the fault of author, not the material with with they work; and that's also helped strengthen my love for Halo as a whole - even if I'm not completely enamoured with the latest production, Halo isn't tarnished for me, only my opinion of the author(s) :)

Anyway, the connections in ILB really helped flesh out the 'humanity' of Smart AIs, their origin, how they interact with humans, and how they're nearly indistinguishable from us in their personality; yet showed how powerful they really are. It's like, as an AI, they wear a human-like facade only in order to be tangible and communicative with us (though it's not by their own choice - it is simply who they are), otherwise they can be overpowered destructive forces if they get out of hand. I love that dynamic combined with the method in which they're created - a unique entity, from a raw human mind.

The drama regarding the creation of Durga, about children, and family, and what makes them and us who we are...

It's the kind of story that really had the full effect for people who played the ARG and lived it daily, weekly, from the flash of "ilovebees.com" in the trailer to the Halo 2 live training events coordinated by Durga... Anyone can read over the campaign, take in the audio drama, all the puzzles and interactions that happened, but it's just not the same experience. It really was a once in a lifetime story that took place, in real-time (and in story time) back in 2004.

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Expanding from that, Sadie's Story was a next great hit - somewhat in line with ILB. A different storytelling mechanic, a different context, different perspective within the Halo universe; tied to core grander narrative elements, but composed of writing that really developed its characters, atmosphere, and events.

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On a more text-based level, the Iris & Halo 2 terminals were awesome; relatively short and sweet, and yet teasing a promise of a much, much greater story; an epic scale series of events we hadn't yet truly grasped. And merely in the form of communications and logs. Who needs novels? =P

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But yeah, some of the other stories mentioned in comments above really do hit the spot, as it were. But these unconventional stories set in the Halo universe really stick out for me.