Moral dilemmas and temptations, relationship friction, duty and responsibility, increased pressure and ticking clocks, dangers and threats

The character being forced to steal essential supplies, such as medicine or food, to survive
Needing to steal an item to build a machine or piece of technology that will save many lives
Having to steal documents to create false papers so the character can flee oppression
Needing to "borrow" someone's keys, password, or access codes to gain necessary information
Having to procure weapons or munitions to even the playing field and enable a rebellion to succeed
Appropriating a car to get somewhere quickly before a critical deadline expires
Taking resources from the wealthy and redistributing them to the poor (a Robin Hood scenario)
Needing to procure an item to trade for something even more vital

Conflict with other characters over the necessity of the theft
Encountering unforeseen issues (a security system in the form of a three-headed dog, the items not being where they're supposed to be, etc.) that complicate the plan
Receiving minor injuries during the process 
The character getting caught and having to talk their way out the situation
Accidentally stealing the wrong items or not enough of them
Being partnered for the job with an impulsive, clumsy, or scatterbrained accomplice
Having to keep the plan a secret from others
Discovering a competitor is trying to collect the same resource
Additional responsibilities being added to the mission (transporting refugees, taking a kid brother along and showing him the ropes, procuring other items that increase the risk, etc.)