Paying off a financial debt
Returning something that was borrowed
Financially repaying the person who supported one monetarily for a time
Serving someone who saved one's life or the life of a loved one
Repaying the caregiver who offered love and support when one was a child or during a difficult time
Honoring someone who made a great sacrifice for one's people
Returning a favor granted by a friend or neighbor (tit-for-tat)

There are five basic human needs that, when missing from a character's life, could motivate them to pursue this goal. The following needs are all possibilities, but only one of them should be the primary driver for any given character. For more information on the relationship between human needs and outer motivations, please see this Character Motivation tutorial.

Self-Actualization: This need comes into play when a character is driven by the need to do what's right. They may have no great personal or emotional connection to the person in question, but their need to be honorable and do the right thing may push them to repay the debt.
Esteem and Recognition: A character's esteem may suffer when they realize they have taken advantage of a benefactor or relied on that person to support them. To regain their self-respect, they will often seek to repay the debt out of a desire to prove they can stand on their own two feet.
Love and Belonging: When a great sacrifice is made, the beneficiary of that sacrifice is often filled with a sense of love and loyalty. The desire to repay a debt can easily arise from the need to show that love and grow in affection toward that person.