I've heard of Kyon Big Damn Hero, never read it myself but I'm not a huge fan of haruhi so that's probably why.
As for favs and recommendations I have two of the former and heaps of the latter so here we go
If anyone likes Tales of Symphonia here is a phenomenal fic on of my all time favourites
Mental Holiday. It's a seven chapter story with each chapter uploaded as a separate story, you'll see why when you start
set after the game it delves deeply into the history Zelos and Sheena have with each other especially Zelos' backstory and then goes for gold by showing how everyone is doing after the last battle while writing one of the most complex, believable and heartrending love stories I've read in a long long time. Sheelos for the win!
I'm a fan of the Marvel cinematic universe and Thor was one of my favs, this fic here
Terrestrial Constellations picks up where the movie finished and carries on, a great read and the relationship between Thor and Jane is handled very well.
These two fics are about my favourite couple in Bleach, Karina and Hitsugaya *squee*
Catalyst has a different take on how they might have met under slightly different circumstances than canon.
The First Time They Met is a complete AU story and unfortunately is unfinished at the moment. So is Catalyst but they are both being updated if irregularly -the authors do have lives
Presents is an adorable fic about Sakura and Syaoran after the finish of Cardcaptors. There are some grammar errors but please don't let them put you off, it's so charming and sweet, it's really worth a read.
Digimon fans, particularly T.K and Kari fans should all read
Final Hope. It's sort of linked to the Myotismon battle in that it goes deeper into the unusual powers the crests and digimon of Light and Hope have as well as giving a nice nod and backstory to the Dark Ocean plot that was never finished in the second season.
Blame the Dog is a hilarious Gundam Seed fic chronicling all the trouble Cagalli gets into (particularly with Athrun) because of her damn uncontrollable dog. Worth a read just for the giggles.
I can not tell you how much I love
Fuu Hououji, Occupation: Hazardous, it is the other of my aforementioned all time favs. This is an AU rayearth fic with the characters split into two clans cursed by a dying priestess, intricate plot threads and relationships and a really good ending. Love it, love it love it.
Munto is a rather obscure anime I think but its really worth a watch.
King of Dreams was written after the first two OVA's came out but before the TV series so it could technically be called AU but eh it's just as good as canon in my opinion. It carries on from where the second OVA finished and has a sequel
To Wake which is even better.
Wenching 101 is just a funny Sailor Moon fic with the Shitennou (four generals) going out girl hunting and giving Darien a few pointers, hilarious if only to see how everyone ends up and with who.
Finally (yes finally lol)
Guardian is a spirited away fanfic that is set after the movie and has a really really creative idea about how Chihiro and Haku end up together in the real world. Ties in with Japanese folklore a bit too.