Well, some non-Harry-centric storied I've enjoyed...
linffn(11230962) Son of the Archer, a crossover with the MCU. In this story, Ron Weasley is separated from his parents when just a toddler, and ends up adopted by Clint "Hawkeye" Barton. Harry does not appear until the sequel, though Neville and Hermione end up playing crucial roles.
I like this story because while Ron does get to grow up on the SHIELD helicarrier and meet a lot of MCU characters, and have his own side adventures while the plot of the Avengers movie happens, he never becomes a miniature soldier. He's still a kid, and when danger strikes, the SHIELD agent's reaciion isn't "Kick his ass, Ron" but "someone get the kid to safety!"
linkffn(9783012) Reign of the Serpent is a massive AU where the wizarding world is ruled by a seemingly-immortal Salazar Slytherin, and the wizarding world is split into castes, with the Serpent caste on the top and lowly Mudbloods at the bottom. Tom Riddle is the Headmaster at Hogwarts, Dumbledore is an outlaw and revolutionary. But Hermione Granger, now living at at a Mudblood orphanage, is determined to rise above her station and get accepted to Hogwarts... and maybe just overthrow the entire society while she's at it.
It's pretty different, but I like it. Most HP characters appear, and most of them are still themselves, just altered from living in a different world. Hermione's the clear main character, though Harry does play an important role... as do Ron, Neville, Dean Thomas and Justin Finch-Fletchley.
linkffn(10705988) A Very Secret Diary is CoS told through the entries in Ginny's diary and her conversations with Tom Riddle. An old fic (Ginny's real name is given as "Virginia") but it's still very good... and creepy as hell, as Riddle manages to charm, manipulate and slowly take control over the poor girl.
linkffn(2594688) Eternal Sunshine of the Scourgified Mind is sort of centered around Harry, Ron and Hermione, though as the fic goes on Ron becomes the definite main character.
Essentially, after defeating Voldemort, the trio are separated and suffer a weird memory loss; forgetting everything that has to do with magic. This means that Harry and Hermione remember only their childhoods in the Muggle world; Hermione goes back to her parents and tries to cope with memory loss, Harry finds himself out on his own with a Dursley family who insist he doesn't live with them anymore... and Ron, who vaguely recalls that his name might be Ron but nothing else, ends up in a mental institution. While there are a lot of heavy themes to the fics, such as frank discussions on depression and suicide, it never gets too bleak, because even with memory loss Ron's a snarky smartarse.
linkffn(3979062) Hogwarts Houses Divided is a next-gen fic... well, sort of. The main character is Teddy Lupin, and the fic chronicles his first year at Hogwarts. Inter-house relations are at an all-time low; nobody gets along and everyone especially hates Slytherin -- and the Sorting Hat has had enough: Either you people learn to get along, or I quit the Sorting business.
While the focus is definitely on Teddy and the kids (some of them relatives of familiar character) pretty much every surviving character from the books comes back and gets at least one moment in the spotlight in this story. Some people get more focus -- Harry has an important supporting role as Teddy's godfather, and Neville is Head of Gryffindor.