Airport design standards try to to take into account the operation of airliners with large wingspan. Basically, the standards like the FAA Advisory circular 50/5300-13A - Airport Design and ICAO Aerodrome design and operations require certain minimum separation distances between the runway/taxiways based on the wingspan of the aircraft being operated there.
The aircrafts are separated into different groups based on their wingspan. For example, the following table is from the FAA AC 150/5300:
Table from FAA AC 150/5300-13 Airport Design.
The ICAO definitions are more or less similar. Based on the most demanding dimension (like wingspan) of the aircraft expected to be operated in the airport, the airport facilities can be determined. For example, the minimum recommended separation distances can be determined from the following table:
Table from FAA AC 150/5300-13 Airport Design.
In case the airports with lesser separation distances (as is the case with many older airports) , the aircraft can still be operated if it is found that the separation doesn't affect the normal operations. From ICAO Aerodrome design manual:
Taxiway minimum separation distances
3.8.7 The separation distance between the centre line of a taxiway and the centre line of a runway, the centre line of a parallel taxiway or an object shall not be less than the appropriate dimension specified in Table 3-1, except that it may be permissible to operate with lower separation distances at an existing aerodrome if an aeronautical study indicates that such lower separation distances would not adversely affect the safety or significantly affect the regularity of operations of aeroplanes.
Another point to note is that the dimensions of aircraft also affect the airport aprons, building separation etc.
One of the most important problems during the induction of A380 was that the aircraft, with a wingspan of ~262' is at the extreme end of the dimensions considered for airport design; in fact, the airport dimensions was an important design consideration in the A380. Still, it was expected that the A380 operation will be severely restricted because of its dimensions.
To this end, the A380 Airport Compatibility Group (AACG) was formed to study the capabilities of airports to handle the superjumbo. It identified airports that can accommodate the A380 during normal operations, and those airports which were considered for planned alternates for A380 (in which case, the A380 is required not to disrupt the normal operations).
The group found that the operations of A380 in runway/taxiway would affect other traffic due to the huge wingspan of A380. From the draft document, which considered the ICAO standards:
e) Taxiing of an A380 on a parallel taxiway, runway – taxiway separation is 107.5 meters,
The A380 wingtip will infringe the runway strip with a distance of 7.5 meters. Operations on the runway should therefore temporarily be halted until the A380 has left the parallel taxiway.
f) Taxiing of an A380 on a parallel taxiway, runway – taxiway separation is 182.5 meters,
The A380 wingtip will infringe the runway strip with a distance of 7.5 meters1. Take-off operations can be operated as normal but instrument landings may temporarily be halted until the A380 has left the parallel taxiway. Non instrument landings however could be operated normally
In the end, this required the regulatory authorities to give waiver for operation of A380 in airports not meeting the spacing requirements. This is not unique for A380. Boeing also considered operations from existing airports for 747-8 which has a larger wingspan compared to 747-400. The result is either a waiver or changing the operational procedure; Boeing notes:
In some cases, airports can accommodate the airplane on the airport movement areas through the use of operational procedures. For example, when a 747-8 is taxiing, operations on a parallel taxiway that is built to less than the required separation standards may be limited to airplanes with a smaller wingspan in order to maintain adequate separation clearances.
Basically, Boeing concludes that operating 747-8 is possible in all airports operating 747-400 (whose dimensions are used in planning separation distances in a number of airports) by getting a waiver after carrying out a study or a change in operating procedures.
Aircraft manufacturers are aware of the issues due to separation requirements as the wingspans get ever larger. For example, Boeing is offering an option of folding wingtips in the next version of 777.