I didn't do it too much with Oblivion(only a few I wrote something for, either outside the game or with a journal mod), but even when I first played Skyrim(I'd already seen Dawnguard, Dragonborn and half of the MQ in Let's Plays by that point - but that wasn't stopping me from playing even if I knew the stories, I wanted to play through them myself), I had already written an entire backstory for my character, before I even got the game. With almost every character I've created in Skyrim, I might not have a story in mind in full detail when starting the character, but soon after I've written something to get me to want to keep going with the character. Even with characters who have started off the same way(most of these with the Live Another Life mod), I've written their purposes and motivations differently. Mostly by using some or all of the details that the starts provide, but sometimes just ignoring the details, using whatever fits for the character.
Claudia, Jayce and Moria all started with the Camping In The Woods start, each of them having different stories. Claudia was briefly a member of the Imperial Legion, but left a year or two before she came to Skyrim, which proved to be a foolish choice on her part, considering the Civil War - which she did not want to involve herself in(and did not). For Jayce I have not ironed out the details yet, but perhaps she left Valenwood(as she has no wish to share anything with the Thalmor, even her own homeland) and drifted for some time before coming to Skyrim, hoping she could get some peace and quiet. Moira is a bit of a different story, given that I used the start for convenience to become a Vampire quickly, since the story is(I have posted this elsewhere on the forum) simply that she came to Skyrim looking for her brother, and she found out that he became a Vampire soon after he left the Legion proceeding the Great War, and he made her one soon after - in game this was a bit different, but the story does work, I think.
Jeune started with the Vampire start, the story being that perhaps a few years before the events of the in-game story, she lost her family and her lover, and rather than the Vampire killing her, he offered her Immortality. Weeks before the game starts, the group of Vampires she was with begins to hear rumors of the Dawnguard, and a few of their members never returned after leaving. After her "Sire"(Or whatever term fits in TES) takes a number of the group in attempt to find and eliminate the Dawnguard, he and the group were not heard from in over two weeks, and then Jeune finds a note and a pile of ashes outside Mara's Eye Pond, the pile of Ashes still having a Runed Axe stuck into it. The note describes that while her creator did find the Dawnguard, he and the rest of the Vampires he took with them where eliminated. This left only her, and two other members(fitting with the two in the game when you start) in the Pond hideout, and the note also said that the Dawnguard knew of the location. After she shared this information with the others, she eventually heard them plotting to kill her and leave. A night or two latter, she strikes first, killing them and leaving herself.(This pretty much being part of the game - and an excuse to get a set of the Vampire Armor). Oddly enough, her first motivation upon leaving? To find the Dawnguard herself, with the rumors she has heard.
While all this seems like it, for the most part, I don't exactly roleplay the game. In some respects, I do. But in others, I don't or just can't. Some of it has been helped by mods, which add the functionality so the roleplay is possible. Especially between Better Vampires and Moonlight Tales(especially so you can have a similar fur color to the character's hair) for these four characters. But in terms of story, I really don't like the idea that you want to "just say it happened". Like if you want a character to be completely unable to learn magic in the game, but the game has no such restriction, and it might not even fit with the lore. If modded in, then I think that works(even if I would not go with that myself), but otherwise, I think it's a unnecessary limit that is too arbitrary for me. Mostly, I prefer things being actually in the game, and don't really want to add it to the story if it isn't. If it is in the backstory or events that lead to the in-game ones, okay. But something during the events of the game? I would rather not.
Though a common trait I seem to be adding in some of these stories is a meeting at some point with a curious individual, which is pretty much one of my Oblivion characters, whose story is the same as the accepted canon for the CoC(though using his original appearance, instead of this game's depiction). Rather than something devious, he is basically pointing them towards their eventual fate, sometimes with interesting outcomes - like with Shan-Tae, who was a Scholar that was a bit into Necromancy, and when she came to Skyrim looking for a certain Alchemist, she was basically told it was suicide to try and follow that path, if not impossible. But then an unusual man sells her an interesting gold/bronze orb, which he suggests will lead her where she wished to go. The catch? Once used, it broke. She still foolishly kept going, and in finding who she was looking for, she nearly got herself killed.