Personal favorites, part 3: Timetravel, dimensional travel and similar
This contains fics centered on timetravel (but not fics centered on "Harry travels to the past and falls in love with..."), fics that have Harry send something back in time and fics where canon-Harry ends up somewhere else.
Amulet of Time series by Luna the Moonmonster.
Harry/OFC, Harry/Ginny, Hermione/Ron. After GoF Hermione gives Harry an ancient amulet. When he invokes it, Harry, Hermione, Ron and Ginny are transported back in time to the Time of the Founders. Before they can return to their own time, they need to spend one year each in the Founders-era, Grindelwald-era and Marauders-era.
PG-13. Four parts are complete, fifth part (post-Voldemort, new story-arc) is WIP (most likely abandoned).
Death, Destroyer of Worlds by Lady Foxfire.
What would happen if someone had interfered just before Pettigrew framed Sirius?
Different Timeline by Crys.
Harry/Padma. Harry wakes up to find the world changed around him.
new Sequel Life in a Different Timeline by veraklon.
Flashback by Amiable Dorsai.
Harry gets a surprise visitor.
The Founders' Heir by Renatus.
After OotP Harry gets attacked by Voldemort at Privet Drive and vanishes, only to reappear several months later. He has spent those months in the time of the Founders, learning new magics and has been given a special duty, to deal with Voldemort. (We never see Harry in the past but it plays an important part and is constantly mentioned.)
Harry Potter and Fate's Debt by Intromit.
Harry/Ginny. Just before Harry parts for Hogwarts when he's eleven, he finds a letter from himself "Get to know Ginny. Fated owed me." which leads to him and Ginny soulbonding the very instant they meet at the station. Starts out close to canon and diverges more and more.
An edited version can be found here though for now it only includes the first couple of chapters. (As good as the idea for the original story was, the edited version is even better.)
Harry Potter and the Nightmares of Futures Past by S'Tarkan aka Viridian.
Harry/Ginny, Ron/Hermione. 30-year old Harry has finally defeated Voldemort. But everyone he ever cared for is dead. Risking everything he sends his mind back in time to his 11-year old self who is just starting to attend Hogwarts.
Harry Potter and the Time Mage by MaxFic.
Harry/Ginny, Hermione/Ron. Harry finally understands the power the Dark Lord knows not but it's too late to use. Risking everything he rewinds time to live his time at Hogwarts again. (post-OotP, no HBP).
Harry's Second Chance by DrT. Or here.
The Last Battle has been fought, and Harry Potter has won. The price, however, has been high. Too high. Nearly every person Harry cared for is dead, maimed, or otherwise injured. The magical culture of Britain might never recover. Luna Lovegood, however, knows a secret which will give Harry a second chance, a chance to make a better future for himself and for most of the people he has cared about. 18-year old Harry's mind in 10-year old Harry's body.
The Mirror of Maybe by Midnight Blue.
Harry/Snape. Post-GoF. Harry gets drawn into a mirror and during his short stay in there lives several years. When he gets back, he has the memories and reflexes of his future self but still the body of his teenage self.
WIP. NC-17. (Unfortunately updates are few and far in between but the story is absolutely brilliant.)
new Möbius by geneticallydead.
Harry/Snape. Ten years after the fall of Voldemort, Harry Potter returns to Hogwarts, celebrated as the saviour of the wizarding world. In the history books, Harry Potter stood over the hollow corpse of Lord Voldemort, vibrant and triumphant, and incinerated that withered old body to the depths of hell. The real truth was, Severus Snape killed Voldemort.
Parallels by BobMin.
Harry/Hermione. Harry has won the war and lost everything he held near and dear. In desperation he gambles everything on a dimensional jump. Can Harry find what he needs to heal and be happy again? Some changes are minor, others are profound. Massively AU, Not HBP Compliant.
Time to Spare by EmySabath.
HBP-compliant. Harry and Draco both get thrown 20 years into the past, ending up in Harry's parents seventh year.
Torn Away: Scenes from a Memory by Tradiferis.
Harry/Tonks. The war is lost, Voldemort is about to kill Dumbledore and Harry when Dumbledore in a last desperate attempt sends Harry back in time with the order to change one small thing. But Harry is obliviated before the timeturner activates and while he remembers who he is, he has forgotten several things of the future...
My other lists.