I can guarantee not everyone is going to agree with my choices, but upon going through my collection of Kataang stories, these were the ones that stood out to me. Not to say they're all perfect, and some are certainly better than others, but these are my favorites, and the ones I would recommend to other Kataang fans.
So, I hope you enjoy!
Post-Series
Fanfics set after the series is over. This is pretty basic.
Jade Bending (Cricket Songs)
This story has a pretty absurd premise, but it's just absurd enough to be something Aang came up with, and somehow I can see it working.
Traditions (Maiden of the Moon)
Okay, I have to admit, I love a well-done 'comedy of errors' fic, and this one does a good job of turning Aang and Katara's wedding into a complete disaster zone.
Eight Years (scorpiaux)
A good take on Aang misplacing his own thoughts and feelings, and Katara somehow being the one to sort it all out (where have we seen this before?).
All About the Reason (netbug009)
Aang, and poetry. There's a recipe for disaster right there. Toph's perspective has the added effect of noticing what a bad idea this is.
Surprises (DJNS)
I believe (correct me if I'm wrong) that this is not part of this author's longer arc. It is an interesting look at Aang and Katara dealing with a first pregnancy (I'm normally not a fan of the kidfics, but this one I like).
Reshape the Clouds (Omoni)
This is an assorted collection rather than a Kataang fanfic, but I think enough of them are Kataang that I can rec it. Omoni has a way of capturing the character of each person in her story that I really love, and she does Kataang beautifully (also Maiko and Sukka and a whole variety of other pairings).
Buttons (HeyItsMJ)
This is more of a series of connected vignettes than a fic, but I love the progression of Aang and Katara's relationship here.
Because (HeyItsMJ)
Aang might be a little slow on the uptake here, but once he catches on to something, he's pretty good at playing by the rules.
Between the Lines (Juxtaposie)
A lovely little take on that very important time in a married couple's life. The awkward moment at the end is done wonderfully.
Signs That Can't Be Learned (Artemis Rae)
Another babyfic - but really, more a look at Aang and Katara and the way they tiptoe around the topic that they both have on their minds.
Turnabout (The Croc Shop)
There are quite a few fics that dwell on Aang growing up and turning out to be hot - but this one managed to make it sort of funny, and of course Katara's revenge was even more so.
What Love Is (JESUSFREAK-And-Proud-Of-It)
The awkwardness of a new relationship, what it means, how you're supposed to act, and the question of whether or not they are in love. This is my kind of fic.
Can't Take the Distance (angelchan-2004)
I'm not normally a fan of 'Aang goes off and leaves Katara behind' fics, but this one is lovely and the overwhelming feelings Katara has when he returns are so poignant. Of course I love the conclusion they come to at the end as well.
The Snows of Yester-Year (wherewulf)
A really cute little ficlet with Aang and Katara keeping each other company during a blizzard, complete with a pretty amusing ending.
Instructions for Dancing (The Flowergirl)
My favorite part of this drabble is the location of Aang's pants. The rest of it is lovely as well, but I just found that so funny!
A Day in the Life (MadLori)
This is one of the most refreshingly simple and yet beautifully told stories in the fandom. Just another day in the life of the Avatar's girlfriend... Never a dull moment.
The Avatar and the Firelord (DJNS)
Probably the best-known Kataang fanfic saga out there, and certainly one of the most enjoyable multi-part fics I've read for them. The story is mostly plot, but with a heavy focus on Kataang (as well as Maiko, some Sukka, and a surprise pairing for Toph), and she writes them very well. It also has the following sequels:
A Week With the Bei FongsThe Value of SharingAn Auspicious BeginningComing of AgeComedy of ErrorsThe First Night (mature)
Smoke and MirrorMaking Up is the Best Part Alternate Timeline
Fanfics that change how things happen in the series (ie, Aang and Katara get together before - or after - they actually did in the series).
Disapproval (mistresskatara)
The midnight conversation between Sokka and Katara in this fic was an interesting idea, and in many ways overshadows the Kataang element. Still, Aang and Katara manage to be cute. Takes place during their stay in Ba Sing Se.
Of Warpaint and Whispers (Lyralocke)
An absolutely adorable take on Aang having to paint Katara's face for her while she's masquerading as the Painted Lady.
Dangerous (Lyralocke)
One of those stories where Aang leaves the others behind "for their own good". Several years later, Katara decides to call him out on what a moron he's being.
An Arrow to Home (MavsGirl22)
Somehow, I just can't resist this idea of Aang bottling up his feelings for years and the two of them having an awkward, tentative courtship as young adults.
The Price of Falling - in progress (Rast)
A look at Aang and Katara coming to terms with their feelings for each other, and what happens afterwards. Absolutely gorgeous fic.
Breath of Silver, Heart of Gold - incomplete (moira2)
Aang learns not to be afraid of firebending, and Katara struggles with her growing feelings for him. I really, really wish there was more of this, because it's lovely.
Alternate Universe
Fanfics that take the characters out of the context of the series and into context of the author's choosing. Anything from changing certain characters' roles in the story to putting the characters into a completely different world.
Reconstructed Destinies (DJNS)
For anyone who's wondered what might happen if Zuko had been the Avatar and Aang had been the Fire Nation prince. This fanfic is pretty darn epic.
Parlor Tricks - incomplete (Lyralocke)
A retelling of the series in a late 1920s Chicago setting. Generally, I'm picky about AUs (ironic, since I used to write so many) because all too often the characters are OOC or it's just an excuse to throw them in high school and have them go to school dances or something. This one manages to be relevant, and I really enjoyed reading it.
Only A Kiss - in progress (The Flowergirl)
I don't normally go for high-school/university fics for Avatar, because I just have a lot of trouble seeing the characters in that kind of setting. This one actually is well-written, though, and anyone who's into this genre of AU should defintely check it out.
Missing Scene
Fanfics that take place behind the scenes of the actual series (ie, no disruption to canon).
The Wall (schellibie)
Probably one of the best takes on the time Katara and Zuko spend waiting to hear from the others. The style is very light and simple and a pleasure to read.
A Different Light (DJNS)
Contains some Taang. It was good to see more bonding between Aang and Toph, which didn't happen a lot in the series. The Kataang, while only present in spirit for most of the fic, was still very nicely handled.
Labyrinth (HeyItsMJ)
Aang and Katara (separately) in the aftermath of the Ember Island Players conversation. I like how this interprets their thoughts and feelings.
Reassembled (Artemis Rae)
All the reunions we didn't see (but wanted to) after the final battle. These are short vignettes, but powerful, and the Katara and Aang reunion was very cute.
Stolen Moments (Fleur Princess)
I've seen a few "Zuko observes Aang and Katara", but this one managed to have more of the right feel to it than some of the others I've seen.
The Lesson (Amira Elizabeth)
One of the cutest 'awkward romantic moments during a waterbending lesson' I've read!
Mature
Sexy stuff going on. Not for kiddies.
Desire Breeds Desire (Rast)
The style of this fic is sweet and moving and beautiful. It's also incredibly sexy. I imagine it takes place a few years after the series, and so qualifies as Alternate Timeline.
Midnight Labors (Artemis Rae)
A nice steamy moment between Aang and Katara. The ending is highly amusing, but I gotta say I enjoyed the buildup very much.
Just Desserts (Juxtaposie)
This fic does a lovely job of building up the tension between Aang and Katara, and the cake batter makes for a tasty prop! The ending wins the whole fic, though.
Tense (Eileen Hearts)
One of those awkward moments that I enjoy so much in fic. A first-time exploration fic for Kataang, which is always fun.
A Temporary Insanity (Juxtaposie)
Probably one of the more amusing takes on Aang and Katara sneaking off for a moment and Sokka threatening to walk in on it.
Closeted (Artemis Rae)
If you can't guess where the quickie in this fanfic takes place, well... go ahead and read it to find out. Another sexy little humor piece.
Bittersweet (Tantrus)
Comfort sex after a difficult fight. It's so easy to get into the moment here, and completely believable that it'd lead to this.
Boredom and Indecency - incomplete (Aang'sGreyEyes)
Lots of good sexual tension built up here - I wish the author would continue this one!
If you know of any other fics you want to rec, leave a comment! I might've forgotten a few really good ones. And even if I don't add them to the list, people looking for good fanfic can still browse through the comments and check them out.