Shin Megami Tensei: Persona
Probably the most underrated, but one of the best series I've played that I personally think outranks the Final Fantasy Series. I stumbled upon Persona 2 many years ago and was interested when I read the back cover and bought a copy. For a long time, I kept the game buried under other RPGs that caught my attention at the time, but finally went back to it and wondered why the hell I didn't give this game a chance.
I was really surprised when Persona 3 came along. While it had a few flaws, it was overall a very good and different game.
Then came Persona 4. Really, I did not expect to like this, considering it was basically a rehash of Persona 3 and I didn't care much for the ending of Persona 3. But the game blew me away, mainly because everything that was good about Persona 3 was kept and everything bad about Persona 3 was fixed and made for the better.
Most of the fanfiction here is really Persona 4 based, but you may see one for 2 and 3, and maybe the original game thanks to the re-make of the original for the PSP.
Persona 4
Honestly, I really don't like the 'fandom' preferred pairings for this game. I'm more of a Souji(Main Character)/Yukiko fan, but those fics are so rare and in between. I like some 'family' fics with Souji, Dojima, and Nanako as well as Souji+Yosuke fics, but really, only as BFFs.
But I ended up caving in and started reading non-BFF stories of Souji and Yosuke. Wow, just holy shit, some of the fics really surprised me. Still, I really prefer the 'best friends' stuff, but I really did not expect to like the stories I read, not just because of the pairing but because I thought it would be a melodramatic roller coaster. They are, but unlike a lot of fanfics with cliche angst, these fics are so painful and realistic that some of them really left me speechless and quelled my angst bug.
But probably the best thing about this pairing is that I've seen them flipflop and their relationship is more as 'equals' than overly seme/uke roles, which makes me very happy and it keeps true to how I saw them in-game.
A lot of the Souji/Yosuke fics came from a Livejournal anon ficwriting community called badbadbathhouse, which I stumbled upon by accident. In my opinion, it spawned a LOT of excellent writing and until I know who the author is or if it's hosted elsewhere, I'll fix the links. You'll have to follow the comments for multi-parter fics.
Also, be warned, a lot of these stories are NC-17/Adults Only ratings, and quite a few have a lot of squimish content, so if you don't like things like BDSM, Rape, Incest, etc, you'll want to avoid the AO content. I tried to warn for it without spoiling the story, but some of them, I really can't, because it spoils the entire story.
Want to be Close by TysonGranger T (Souji/Yukiko) - A very cute and innocent sort of story. Basically, Souji pays nightly visits to Yukiko at and speaks to her. I think this story tells a lot more because it lacks smut and it will tickle your fluffy bone.
Life's Deductions by FortunesRevolver T (Souji/Naoto) - I'm not really hung up on this pairing, but I really liked this story. Basically, it's Naoto's feelings through her social link in an intimate setting. So basically big massive spoilers if you haven't done her social link.
Walking on Vapor by qfisher M (Various pairings) - Probably one of the better AUs I've read. Basically take the Persona 4 cast, but make it so the murder takes place 20 years later. Things are much different and it's refreshing to see an AU that's very well written. There's a lot pairings in this, so I didn't say who is with who to avoid spoilers. Definitely worth a read.
Hears the Silence So Loud by Pineapple Gel T (Souji + Yosuke) - This is more Yosuke centric really, as the focus is him and his mp3 player. This is more of the kind of fic I like, where it's more of a 'best friends' thing going on between the two, and it really does show here.
Backwards Parenting by Aphelion-orion T (Implied Souji/Yosuke) - This one had me in a fit of giggles. Basically, Dojima tries his parenting skills when he catches Souji and Yosuke doing... naughty on the couch. It... sort of doesn't work out. A nice story that will give you a fit of the giggles.
Things Found by Anon AO (Yosuke/Souji) - This story is just... really funny. It had me laughing. Basically, Yosuke finds a certain weakness in Souji and exploits it... to the max. The ending with Rise is funny as well.
Kill or Cure by Anon AO (Yosuke/Souji) WARNING FOR QUESTIONABLE CONTENT - This story is painful, period. It manages to stay angsty but not turning in a melodrama, mostly because I think the problems the characters are going through are painfully realistic. When I first saw the prompt, write a fic with one of the characters having a food disorder, I really didn't want to read it. But I did anyways, and... wow. Just fucking wow. Be warned, there's a lot of angst, character death, some really gross moments, and... other questionable stuff. If I said what, the entire story would be spoiled, but if you're squmish about some things in fanfiction, you may want to avoid this.
Pain by Anon AO (Yosuke/Souji) WARNING FOR BDSM AND RAPE - Another very heartbreaking story that I actually wasn't going to recommend at first, because the story involves BDSM and makes it seem like a 'bad' thing (So if you may get offended by that, skip it). But the overall suspense, especially near the end, is what really got me hooked. Basically, it's a big story of misunderstandings.
No Beginning, No End by Anon M/AO (Souji/Yosuke) WARNING FOR CHARACTER DEATH - This was actually the first story I read on this pairing and I'm really glad I did, because this story not only has angst, but it has a plot that actually reflects the game somewhat. Basically, Dojima is dead and now Souji has to take care of Nanako. One thing I like about this story is that it follows the 'Normal' Ending and it also assumes you didn't max your social link out with Dojima, which I think was very creative.
Out of Service by Anon AO (Souji/Yosuke) - This one is probably my favorite, because it's not over-the-top angsty like the last stories, but provides enough angst that you'll be satisfied. Basically, Souji and Yosuke meet again in college, only they don't know it's the other. I really liked the timeskips in the story too and how it all ends up neatly in the present time. This story is told from Yosuke's PoV.
Every Day's Great by Anon AO (Yosuke/Souji) WARNING FOR CONTENT - I normally don't recommend fics like this, let alone unfinished ones but... seriously, if you think life sucks for you in the present... yeah, it can get a whole lot worse. When I read the prompt for this, I rolled my eyes. When I read the fic... just fucking wow. You got a lot of stuff going on, besides the prompt, you have Yosuke dealing with a lot of family issues plus the fact he works for basically the equivilent of Wal-mart on top of dealing with Souji. A very intese fic with buckets by the buckets of angst. Not finished currently.
Dicing with the Devil by Anon AO (Souji/Yosuke) - Well, this was a nice treat I woke up to. Basically, Yosuke has a bad habit of betting against Souji. He makes a bet he is sure he will win, but you'd think Yosuke would learn by now not to bet against Souji. Very funny, and I really liked the presents that everyone gave Souji. The plushies I could so see Kanji making. This fic will satisfy just about anything for you from cute fluff moments to just tittering the angst meter to well written smut moments.
Separation by Anon AO (Kanji/Yosuke) - This fic got my attention not because of the pairing, but because of the way it's written. 95% of this story is told through letters, e-mails, chat, Twitter, and blog posts, which I gotta say, was very creative on the writer's part. This story goes from being absolutely funny to shockingly painful. The funny thing is that this spawned through a very simple prompt. AUish to October and beyond's events.