I still haven't gotten around to running a session of Savage Worlds yet but there is a "rule" that really peaked my interest. It is the Interludes rule on page 105 of the Savage Worlds Deluxe Core Rules.
From the book: "The Game Master should run an interlude during natural down-time such as when healing up after a fight, performing research, or between legs of a long trip. To start, pick a player and have her draw a card. The Suit determines the general topics as shown on the Interlude Table. Each entry requires the player to tell a story in the voice of her character. The tale should be substantial enough to take a few minutes and may draw in other characters' participation as well."
Essentially, there are four different topics: Tragedy, Victory, Love and Desire.
Tragedy: A tale of tragedy or misfortune from your hero's past. This could also be hints/clues of a dark secret the character wants to keep hidden.
Victory: A tale of a great victory or personal triumph in your character's past.
Love: A tale of a character's greatest love whether it was lost, found or waiting on them to return.
Desire: A tale about something your character wants or already has.
Savage Worlds uses a deck of cards for this feature but with OSR you could simply use a d4 or if you are more of a White Box kind of gamer just use a d20 to determine the topic for the character's tale.
Tragedy: d4(1); d20(1-5)
Victory: d4(2); d20(6-10)
Love: d4(3); d20(11-15)
Desire: d4(4); d20(16-20)
This would also be a nice "trick" you, the GM, could use when your players do the expected unexpected of throwing the game off course. Put them in a situation and decide or roll to determine which player will be telling the tale. This can give you that extra time to prepare for the unexpected that your players threw at you.