Why are fuel tanks located in wings?
Several advantages:


Wing structures are hollow and voluminous in order to provide structural rigidity against flutter and carry flight loads.  This provides the space needed to store fuel.
On a conventional aircraft, placing fuel tanks in the wings places the fuel mass very close to, or on, the center of lift.  This dramatically reduces Cg shift during flight and reduces the size and weight of the tailplane to maintain stable flight.  It also reduces Cg shifts due to sloshing of the fuel inside the tanks, due to the limited constraints of longitudinal travel for the fuel in the tanks.
In the event of a crash landing, having the fuel in the wings keeps it away from the cabin and the occupants, reducing risks of cabin fires.
The weight of the fuel reduces the loading moment on the wing roots, reducing the weight of the structure needed to support the aircraft during flight.
Fuel stored in the wings either partially or completely eliminates fuel storage in the fuselage, leaving more room for passengers and cargo.


Disadvantages:  

1) Fuel sloshing with in the tanks laterally as a result of turbulence, or uncoordinated flight, can lead to lateral weight shift and potential lateral instability.   At low quantities of fuel, and in prolonged uncoordinated flight, there is a chance that the engine can suffer fuel starvation simply because the fuel has flowed out of the sumps in the tanks These problems can be alleviated with proper fuel tank baffling and the use of feeder hoppers fed by the main tanks which the engine drinks from.

2)  On aircraft which utilize a siphon feed fuel system such as low wing aircraft, the fuel cannot be evenly siphoned from both tanks at once.   This is a particular problem in single engine aircraft, where separate fuel systems are not dedicated to one engine in particular.   In such cases the engine will feed off either the left wing tank with a right wing tank  and this is controlled by means of a fuel selector valve in the cockpit. On aircraft that do not have automatic fuel management systems, engine fuel feed must be manually selected.  Care must be taken to alternate feed from both tanks periodically to prevent a lateral imbalance and fuel quantity. Additionally this fuel tank switching schedule, if ignored long enough, can potentially lead to fuel starvation of the engine and a forced landing.  This is particularly problematic in the low wing light single engine aircraft such as the Piper PA-28 or Cirrus SR-2X, especially if the pilot has recently transitioned into this airplane after flying high wing aircraft, which use gravity feed fuel systems, and allow the engine to feed from both tanks at once.  Larger single engine aircraft like the TBM have automatic fuel tank switching systems to address this problem.   Large multi engine jet aircraft have dedicated fuel management systems which address these problems.