As a teenager I'd do that on the multiplayer maps of Jedi Outcast and Jedi Academy. Never actually played online: I'd just explore the maps telling stories in my head. I also made a trio of roleplaying games using the scenario editor for the RTS Star Wars: Galactic Battlegrounds; given that the warm reception they received was a huge boost to my confidence in my early creative endeavors, I've thought about making another for years--but I never seem to get around to it.
I definitely try to get "in-character" regardless of the genre of game I'm playing (assuming it's character-based of course...).
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But if of ships I now should sing, what ship would come to me,
What ship would bear me ever back across so wide a Sea?
--"Galadriel's Song of Eldamar"