When you finish reading a really good series, the first thing you want to do is find out more about the characters, the plot, and the world. Many people write their own continuations, or changes, to the source material, which is called fanfiction. With a universe as large as Harry Potter's, there are plenty of possibilities for stories. However, since it's so popular, many of the same concepts have been done to death.
This list is meant to be a recommended list of fanfics to read after the series. They're all complete, and hopefully, even if you're already a regular fanfic reader, you'll find something new in here too.
Reclamation by copperbadge
Reclamation by copperbadge is the tale of Tom Riddle, who has renamed himself Tom Gaunt after lost family members and become a professor at Hogwarts. In this version of the story, Professor Albus Dumbledore's good influence with Tom won out, and Tom fulfills his desire to teach, if not his desire to live forever.
He counsels Remus and Sirius in the process and tries to help Severus Snape, though he doesn't quite succeed with that last task. This fic is an interesting look at Tom Riddle and is definitely worth the read.
What to Do When the War is Over by Glisseo
This fanfic by Glisseo concerns exactly what it sounds like: Lily and James making a list of things they want to do after the First Wizarding War is finished. They start it before Harry is born, when Lily mentions going to Wales as a child. James isn't too keen on the idea, but it eventually becomes a way to keep themselves sane in the craziness of battle.
They stick the list on the fridge, and it grows longer as they think of more they'd like to do. This story really hammers home just how young Lily and James are, and it ends on a somber note.
This is For Cassius by MiraSoraStone
This is For Cassius by MiraSoraStone is a beautifully-told fanfic that diverges from canon when Cedric Diggory isn't chosen for the Triwizard Tournament. Instead, Slytherin Cassius Warrington is chosen as Hogwarts' Champion.
You may remember him as a Slytherin Quiddich player in the series. Cassius is a sympathetic figure; it's easy to root for him. The events of the Tournament proceed as in the book, though Slytherin House's reaction to the murder of one of their own is excellently written. The rest of the war spirals from there, just as you might expect.
The Greater File of the Subject by Stoplight Delight
Stoplight Delight by Stoplight Delight has begun a massive fanfic that chronicles Remus Lupin's years at school, and his efforts to be brave in the face of his lycanthropy titled Against the Moon. However, since that fic isn't complete, they've also written so-called Missing Moments, to fill in the gaps for the story.
This one covers Professor Filius Flitwick discovering the truth about Remus during the boy's third year. Flitwick is a non-biased character, having dealt with bullying himself, and his realization that Remus' friends have stuck by him despite his condition is heartwarming.
And the Wolves All Cry by monroeslittle
This story by monroeslittle answers a version of the question of what would happen with the war if James and Lily both survived Halloween night along with Harry. This story also deals with the idea of Harry not being the Boy-Who-Lived. Voldemort deals in more Hitler-like tactics in regards to the Muggleborns this time, and Lily and Harry are put into a concentration camp-like place, where they run into a young Hermione, separated somehow from her parents. James and Sirius are taken to Azkaban. Lily struggles to survive for Harry and Hermione, and eventually triumphs, though not without great loss.
True Form by TheLoud
True Form by TheLoud gives Sirus all the love he deserves, even if it's not what the other characters expect. During Harry's fourth year, Ginny adopts a dog. A very familiar dog, in fact. He's Sirius, and to Ginny, who doesn't know any better, his name is Shadow.
She loves him, but the more time he spends in his animal form, the more he forgets about himself, to Ron and Harry's worry. Some people might say that this story is a better end for Sirius than his fate in canon, though it is still somewhat bittersweet.
Just a Random Tuesday... by Twisted Biscuit
This story Twisted Biscuit is comedy gold. Set during Harry's fifth year, we follow Professor Minerva McGonagall during a very hectic day. She deals with Umbridge, staff meetings, Draco Malfoy, Peeves, and a disappointing lack of hot cocoa.
As the summary puts it, "it's a wonder she's as nice as she is." This is a long, complete, hilarious piece of genius, and it won't disappoint. McGonagall's faith in Dumbledore, despite dealing with his disasters, is touching. McGonagall's day just keeps getting weirder the further you go on, but the story is worth it.
Yes, but by aestel
Yes, but by aestel is a parody of the category of fanfics known as Marriage Law fics. The concept is that magical Britain has too much inbreeding or dropping population rates, so the Ministry has instituted a law: purebloods must marry either half-bloods or Muggleborns, in order to fix the population.
This particular story features the courting of Severus Snape and Nymphadora Tonks. They're serving as guinea pigs for the program, which the majority of magical Britain is against. As a parody, it's hilarious. It also serves as a great characterization of Tonks.
Hogwarts (to welcome you home) by gedsparrowhawk
This story by gedsparrowhawk disregards J. K. Rowling's canon fate for Harry as an Auror. Instead, it gives us the obvious answer: he becomes a teacher for Defense Against the Dark Arts. Told from Minerva McGonagall's perspective, this story shows how Harry settles back into teaching, and back into life after the war.
Hogwarts is heavy on the friendship, as well as how Harry coaxes these friendships into being between students from opposing houses. He starts a Dungeons and Dragons group in a magical school! It's quite lovely, really, and quite recommended.
I Know Not, and I Cannot Know - Yet I Live and I Love by billowsandsmoke
This fic by billowsandsmoke covers the interesting, yet plausible friendship between Severus Snape and Luna Lovegood. It covers Luna's seven years at school, and how her quiet manner changes Snape's mood toward her. He ends up helping her as a potions student, and she helps him with his feelings on past regrets and the future.
It's quite likely Luna is the only character a fanfic like this could be written about with Snape, and this one is worth the read. Luna's character is delightfully accurate here, and Snape is enjoyable enough to read about.