Why was the A380 built with a gull-wing design?
The wings are designed like that. You can see them in the picture below.



Image from airliners.net


The A380 wings are designed to be the most efficient while still inside the 80m 'box' for efficient airport operations. The result is a clean slate design which used CFD extensively to get the most efficient aerodynamic design possible.
The 'curve' near the root means that the landing gear in the wings could be as short as possible while being long enough to prevent a tail strike during rotation and allowing the spar to pass below the floor.
The shape also allows enough ground clearance for the inboard engines. This assumes importance with the advent of engines with ever higher bypass ratios.
Of course, the use of modern composite materials means the the wing 'flexes' up to be more or less straight once the aircraft is airborne.


(wikimedia.org) In-flight 'flex'.