In some fanfictions, there could be external forces that keep Harry and Ginny apart. For example, a powerful dark wizard might cast a spell that makes it impossible for them to be together romantically. Or the wizarding society in the fanfiction could have new rules or social norms that oppose their union, causing Harry not to marry Ginny.
In some fanfictions, Harry might not marry Ginny because the author wants to explore alternative storylines. Maybe they want to pair Harry with someone else to create new romantic dynamics. For example, they could pair Harry with a new character to show how his character develops in a different relationship.
A possible plotline could be that Harry decides to break off his relationship with Ginny before any talk of marriage. This causes a rift in their friend group, with some taking Harry's side and others Ginny's. Another plotline might involve Ginny trying to change Harry's mind by showing him how they could have a great future together, but Harry remains steadfast in his decision not to marry her due to his own insecurities.
One possible scenario could be that Ginny meets an old acquaintance who has changed a great deal and she starts to have feelings for this person while still being with Harry. Maybe they share a common interest that she feels Harry doesn't understand. However, this goes against Ginny's strong character in the original series, so it's a very different take in fanfiction.
In some versions, it could be that Harry has to die to break a dark curse placed on Ginny. He discovers that his life is the key to saving her and willingly gives it up. He might have a premonition about Ginny's fate and decides that his death is the only way to change it. He then confronts the source of the curse and allows it to take his life instead of Ginny's.
In some fanfictions, they might go on adventures together. Exploring the wizarding world more fully, perhaps seeking out new magical creatures or ancient magic. They have a thirst for discovery after the chaos of the war. Harry's knowledge and Ginny's courage would make them a great team on these excursions.
In some fanfictions, Harry and Ginny might fight side by side, using their respective magical skills. Ginny could be shown as a fierce fighter, using her Bat - Bogey Hex to great effect against the enemies, while Harry uses his Patronus to protect them from Dementors if any are present during the battle.
They might get married and start a family right away. In fanfiction, it's common to see them settling down and having kids, living a peaceful life after all the chaos of the battle.
They could have a slow dance under a starry sky charm created just for the ball. Harry would hold Ginny close and they'd look into each other's eyes, lost in the moment.
One possible scenario could be Ginny trying to control who Harry spends time with. For example, she might not like him being around Hermione so much because she's jealous. Another could be her trying to control Harry's actions in the wizarding world, like which quests or missions he undertakes. Maybe she thinks some are too dangerous and tries to stop him forcefully.
It's also possible that they meet at a Weasley family gathering that Harry attends. Ginny, being the youngest Weasley, is a bit shy at first but then Harry says something funny or kind, and that starts their interaction.