Is it possible to do a barrel roll in a large aircraft like a B737? Can the bigger planes like B737 do barrel rolling kind of stunts like fighter jets do? I'm sure if it's full of passengers or cargo it would be very difficult and dangerous, but is it possible with an empty aircraft?

I remember an All Nippon Airways incident where the co-pilot did a 131 deg roll by mistake but I don't know if a complete barrel roll is actually possible in large planes?
Yes, it has been done before in an even larger aircraft, the Boeing 367-80, very famously by "Tex" Johnston on August 7, 1955. This aircraft was the prototype for the Model 707. 

When a barrel roll maneuver is properly performed the aircraft remains in a positive-G state, so no "inverted flight" is experienced by the aircraft. According to the International Aerobatic Club,


  The Barrel roll is a combination between a loop and a roll. You complete one loop while completing one roll at the same time. The flight path during a barrel roll has the shape of a horizontal cork screw. Imagine a big barrel, with the airplanes wheels rolling along the inside of the barrel in a cork screw path. During a barrel roll, the pilot always experiences positive Gs. The maximum is about 2.5 to 3 G. The minimum about 0.5 G.