The A-number 1 thing I care about in any story, really, but especially in the case of fanfic: characters that ring true. I will forgive a lot of other problems in a story if the characters act and sound like themselves. (The converse is also true: a story can be brilliantly written, expertly plotted, amazingly original, but if the characters feel wrong, I can't enjoy it.)
This will by definition have to be true of anything I rec, but here are a couple of stories I particularly like as character studies:
Duty by darkcyan. FFX
One of the first Auron stories I ever read, and one of the most influential in terms of how I characterize him.
Matched Set by domlandbubbles. FFXII
Excellent look at Balthier.
2. Gameplay and/or world-building meta
I am a total sucker for this. To use some awesome terminology that I just learned from pixelnyx, I love stories that can provide a Watsonian explanation to a Doylist problem (see http://tvtropes.org/pmwiki/pmwiki.php/Main/WatsonianVersusDoylist). How does magic work? What's a save point? Why was this character not in the sequel? Tell me these things, and make it follow logically in-world, and you have me forever.
Swords are Swords by spindizzy. FFX-2
How did the Gullwings end up with Tidus's and Auron's swords? And how did they feel about it?
Friendly Monsters by fyre bird. FFIX
What's up with those monsters who give you items, anyway?
3. Answers to Interesting Questions
This seems, to me, to be the entire point of writing fic: exploring the what-ifs that aren't covered by canon. This aspect is often associated with AUs: What if this thing in canon had happened differently, or hadn't happened at all? But I also find good questions to be an important part of post-canon stories, and pre-canon, and scene fillers. What happened while we weren't watching after that? What happened next, or before?
All He Had to Say by The Jack of Spades. FFX-2
What happened to Gippal and Nooj after the Commsphere stopped transmitting?
Zanarkand Sleeps by Princess Artemis. FFX AU
What if Auron never left Zanarkand?
4. The Unexpected
This is where my taste for crack comes in: weird parings, out-there crossovers, unusual sources. But! See above. The story still must be true to the characters. That's hard to pull off, which is why I'm a lot pickier in this category, and why I rarely write it myself.
Make a Metal Gear by K Project. Metal Gear Solid/Katamari Damacy crossover
[ I succeeded in crawling into the breast of my big boss! ] by miss_priss. Maru the Box-Loving Cat
Break by mythicbeast. FFX-2. Rin/Nooj (gen, but with undertones)
30 Days of... Project! Complete list of questions / Ask a question on LJ or on DW.
This entry is also posted at http://owlmoose.dreamwidth.org/502546.html. There are currently comments on DW.