Structural failure of a wing isn't a very common occurrence. As it would immediately lead to a major disaster, you can be assured the manufacturer of the aircraft your flying in has done everything possible to avoid this situation.
Metal fatigue would be a leading cause of structural failure. During the process of flight stress, both up and down is applied to the wing. Over a long period of time this repeated movement alters the molecular makeup of the metals or, as is the case with many modern aircraft, the composite materials used to construct the wing. After some point in time cracks develop and if left unchecked the wing will at some point fail and the aircraft will crash.
Of course mandated regular inspections are in place to prevent this from happening and aircraft may have a predetermined length of service determined at the time of design that limits how long an airframe may be used before it reaches the point where metal fatigue may become an issue.
Corrosion may cause damage to a wing weakening its structure. Dissimilar metals in contact with each other creates corrosion. Operating in a salt air environment may create corrosion. Electrolysis takes place and the result is corrosion. Another reason for regularly scheduled maintenance and inspections.
Impact may cause structural failure, impacting something on the ground, causing unseen damage. We've all seen the World War II footage where the bomber on top drops its load with a bomb falling through the wing of the aircraft below. The wing collapses and the plane goes spiraling down. Be it a mid air collision, or a large bird strike at just the right spot. Damage from impact can cause a wing to fail structurally.
It is conceivable that an aircraft that is designed with folding wings could have a system failure allowing the wing to collapse from its normal extended position. A definite unrecoverable flight characteristic.
The other type of wing failure would be aerodynamic failure. A change in the shape of the wing would affect the lift characteristics of the wing and the plane may become unable to maintain altitude.
The most common reason for this is ice buildup on the leading edge of the wing. Not only is there added weight that may be more then the aircraft is designed to handle, but the shape of the wing is altered as well. With the loss of lift created by the altered shape the aircraft will require more power to maintain air speed required to stay above stall speed. Fall below stall speed and you fall out of the sky.