As a big history and mythology geek, this kind of thing tends to interest me.
If I’m going to have a past, I prefer it to be multiple choice!
Alan Moore, The Killing Joke
Back when Vampire started with Masquerade, the existence of Caine and the Antediluvians and the like was a question mark. But it was in the rulebook, Generation was a buyable Background, there were no alternative explanations forthcoming for several years, and the Sabbat turned out to be all about Caine and the Antediluvians, so it became generally accepted among readers that it was something resembling true. The strongest out-of-character alternative came in the second of the Gehenna adventures making Lilith a much bigger deal.
Requiem took a different tack, offering multiple possible origins for the Kindred, for individual clans and vampires in general, multiple absentee creators, and the Fog of Eternity that jumbles memory and dream for those sleeping in torpor, so nobody still walking around knows for sure. Or do they...? (And it also means you can play a thousand-year-old vampire without maxed-out Disciplines and books-full of ancient lore.)
Each approach can also feature in individual games. Do you write down who the last prince was, or not really think about it until someone asks? Confident improvisation - and remembering that vampires often lie about this kind of thing - can go a long way. But equally, thinking through a backstory can affect how you develop and portray a setting. Thinking even just for a moment about the last prince can present a story hook, or a new perspective on the current prince. Then again, too much nailed down can remove a mystery. Is Boba Fett improved by knowing what his dad was like?
So I tend to fall somewhere in the middle here. If something occurs to me, I’ll make a note of it. Not a big note, probably, but a note.