So one of the common arguments I see regarding Swords & Wizardry White Box and White Box: Fantastic Medieval Adventure Game is that it's too narrow. Characters have no abilities beyond their combat or class related listings to give them any definition, background, or motivation. I regard this as a strength of the system as it keeps things simple - but I understand how it could frustrate some people.
So, I tried to come up with a solution that kept to the core of White Box's simplicity. I give you the One-Sentence Background.
The One-Sentence Background is exactly that. A character's background defined in a single sentence. This sentence must include some form of motivator and some kind of profession or skill outside the character's class.
Example One: Arki the Dwarven Fighter was a Blacksmith who wants revenge for the destruction of his clan.
Example Two: Jana the Thief is a former Woodworker who took to the road to search for her missing daughter.
The profession is something the character can attempt to use as is appropriate to the situation and with Referee approval. This can be narrative, or mechanical. If a mechanical system is used, I'd recommend having the character simply make a Saving Throw, but receive +2 to any saves tied to using their profession.
The background has no mechanical effect. It simply serves as a springboard so players can call back to their character's primary motivation and have a sense of how their character will act in a situation.