Personal favorites, part 1: Family, mentorship, adoption, Severitus, Sevitus,...
An absolute favorite theme of mine is Harry interacting with adults: they can be true family by blood or simply adults who mentor him. Some of the stories in my other favorites also have Harry adopted or mentored by someone but are centered more closely around another theme, so I won't put them up here. Likewise I will not put stories that I find center on family in Sixth + Seventh year even if the story takes place during sixth year for instance.
Blood Magic by gatewaygirl.
Severitus. Minor mention of Harry/Hermione, Severus/Remus. Post Ootp. Sixth year.
Changes by procyonblack.
Dangerverse by whydoyouneedtoknow.
Sirius/OFC, Remus/OFC, Harry/Ginny, Ron/Hermione, Luna/Draco, Neville/OFC, Charlie/Tonks. AU. A few months after Voldemort's first fall Remus (with the help of two OFCs) finds out where Harry lives and how the Dursleys treat him. They also find out that Pettigrew was the traitor and that Sirius is innocent. They steal Harry and break Sirius out of Azkaban. Basically Harry, Draco and Hermione grow up together with Remus, Sirius and their wives. Story consists of Main-story (with several sequels: first part tells the story till Hogwarts, second story the first two years, third story is currently WIP and tells year 3 and 4.), several one-shots (telling stories of Sirius and Aletha, romance-stories written by Sirius, etc.) and AU-stories (yes, AU to the AU. lol) Very original story!
new Family Night by Celebony.
As Hogwarts starts a quarterly Family Night, Harry is determined take part. Facing the heartache of looking in all the wrong places, he'll have to discover the true meaning of family, and that sometimes it comes from where you least expect it.
Warning: this fic had me nearly in tears!
Harry Potter and the Emerald Tablet 1: Awakenings by Lady Alchymia.
Harry/Cho. After OotP Remus takes care of Harry.
WIP-sequel Harry Potter and the Emerald Tablet 2: Psychosomachia Harry/Susan.
Harry Potter and the Enemy within by Theowyn.
Harry needs to take up Occlumency-training again during his sixth year. Slowly his relationship with Snape changes.
new Harry Potter and the Guardians of Power by teacherbev.
Harry gets kidnapped by Voldemort and thinking "Merlin, save me" with all his power and magic behind it, manages to transport himself and Severus back in time to Merlin and the Founders. Severus as mentor to Harry.
While it's more of a Snape as mentor, both Harry and Severus have a good relationship with Dumbledore. And after Snape adopts Harry, Dumbledore adopts Snape, so Harry becomes Dumbledore's adopted grandson.
The first couple of chapters aren't too well written and the author went a bit overboard with Harry being the Heir of all four Founders, Merlin, a multiple elemental, a metamorphmagus,... But nonetheless the fic is quite outstanding: it has the most original way to deal with captured Deatheaters and the greatest prank ever played on Dumbledore!
Harry Potter and the Long Summer by Mirriam Q Webster.
During the summer after OotP the Order rescues Harry from Privet Drive. Dumbledore has no better place to put him than Snape Manor. Snape becomes a mentor to Harry. (Clichéd fic but well written for once.)
WIP-sequel Harry Potter and the Pillar of Storge.
A Knight of My Own by Altaira.
AU. When Dumbledore keeps putting Harry with the wrong kind of people, Severus rides to the rescue. Supposedly pre-slash but mostly Severus mentoring Harry.
Malfoy Child by Vorabiza.
Harry/Draco. Seventh year (not HBP-compliant). Draco gets turned into a 4-year old by a potion and Harry takes care of him. As Snape is Draco's godfather, Harry and Snape are in close contact for several months and slowly Snape becomes a mentor to Harry.
Sequel Summertime Kids.
Malfoy Flavor by Vorabiza.
Harry/Draco, Severus/Lucius. Sevitus. Post OotP. After Harry finds out that Snape is his father he decides to return to school as Dustin Snape for his sixth year while Harry Potter supposedly is off somewhere to train.
Realizations by Wishweaver.
After GoF Harry returns to an empty house, the Dursleys having abandoned him. Afraid that he might endanger his friends by contacting him he hides on his own, befriending a Muggle-family with two witches as daughters.
Resonance by GreenGecko darkirony.
Post-OotP. After Harry defeats Voldemort in his sixth year Snape adopts him. Seventh year and start of Auror-training.
Skin Deep by Vingilot.
Sevitus. Harry/Bill. Post-OotP. Manipulative Dumbledore. Mentions of Harry getting raped by uncle Vernon.
Snape's Invisible Friend by teacherbev.
AU. Harry rescues himself as a baby and chooses Snape as his protector, why no one knows, because the toddler isn’t telling, and no one can see him but Snape. (Usually I abhor AU-stories but this one is outstanding.)
Sequels Growing Up Snape and Shaun Snape: Age 8. WIP.
Unlocking Harry Potter by sarini.
Severitus. Harry/Charlie. Sixth year.
Sequels Finding the Key, Closing the Door
Prequel Release the Wolves.
Web of Lies by Star Polaris.
After GoF Dumbledore takes in a sick Harry. To keep him safe, they pretend that Harry is actually Dumbledore's grandson Alec.
Sequel Web of Lies: Revelations.
When Nightmares are a Good Thing by Rhiane Raine.
After OotP Harry finds out that McGonagall and Dumbledore are actually his grandparents. Why did they reject his mother and him?
A Year like None Other by Aspen in the Sunlight aspenlight.
In Harry's 6th year, a letter from Surrey sends him down a path he'd never have walked on his own. Post OotP. Snape adopts both Harry and Draco.
WIP-Sequel A Summer Like None Other.
My other lists.