I have seen several Airbus A380's takeoff on large runways, but how small can a runway get for an Airbus A380 to takeoff fully without overrunning?
Airbus's A380 AIRCRAFT CHARACTERISTICS AIRPORT AND MAINTENANCE PLANNING data says that for an A380-800 at maximum certified landing weight landing at sea level a 7000 ft (~2150m) runway is required to land (in dry conditions, presumably).
"A380 Briefing For Pilots (Part 2)" shows a 3750m (~12,300ft) takeoff requirement when operating at 600,000kg at sea level, or almost 5000m if operating at 5000ft at 560,000kg (presumably a lower maximum weight for the higher altitude). If you can significantly cut back on the weight (no PAX, no cargo, minimum fuel), the bottom end of the chart says ~1600m (~5280ft) for "I don't know how I got here, but I need to get away".
(Trying to find better numbers seems to be difficult because the computer does the calculations, and one document I found claiming to be an FCOM (Flight Crew Operations Manual) only describes feeding the data into the computer, and fun things like how the plane can audibly alert "Runway Too Short!" when landing, but I didn't find any takeoff or landing charts in the 8,100 page manual).
Here is a video of a QANTAS A380 taking off from Los Angeles (LAX) on RWY 24L headed to Sydney (YSSY/SYD). The aircraft appears to leave the ground at taxiway AA, and using Google Maps' distance measuring tool, the take-off roll distance is 2400 meters / 7875 feet.
For an acceptable safety margin (rejected take-off, etc.), the runway should be at least 500 meters (1640 feet) longer, maybe more. According to airnav.com and the FAA's downloadable PDF, Runway 24L is 3318 meters / 10885 feet long.
Note that this is a 13-1/2 hour flight, so the aircraft is fairly heavy with fuel and cargo/passengers.