I think Oblivion is a good example of this done well. All guests immediately understand the essence of the backstory purely from the theming, there is videos to watch in the queue for those who please but if you miss them, it doesn't detract from the ride. There is a reason why there's a great big coaster track there within the story itself (I always thought Nemesis was a bit of a reach in that respect), and it's an engaging, original (if now a bit dated) idea which doesn't require pages of written explanation.
Big Thunder Mountain is another good example, there is a reason why everything this there, track and cars included, and it is immediately obvious with no explanation required. There is more backstory to look into if it interests you (the whole society of explorers and adventurers thing), but if you have no interest in that, it doesn't detract from the ride.
Dark rides can get away with more detail, because they are essentially entirely storytelling as an experience, with coasters, too much can get a little tiresome though.
I think the art is in creating an experience with a narrative which anyone can understand purely by riding the ride, but creating extra depth to that narrative through detail in the themeing/queue/area.
There is of course the 'just ride the coaster' argument, but I'd say this kind of thing, done well, is what makes me love true theme parks over something like Six Flags.