Sultan Kebab started the whole kebab scene in Seoul. This was way before Koreans started ruining it with shredded cabbage and honey mustard. The founder, Omar, who calls almost everyone "my brother," has become an icon. A tiny little kebab stand only serving one item on a lonely Itaewon street blossomed into two locations with actual seating, lamb on the menu (a major feat in modern Korea), and a freshly introduced sides and desserts menu. Sultan Kebab is hands down the leader in the Turkish kebab drive and continues to strike that balance between authenticity and pleasing the clientele.
UPDATE: Due to some shake ups in ownership, Omar currently runs Ankara Picnic. The flavor of the original Sultan Kebab has changed. It now resides at Ankara Picnic. I'm changing my rating accordingly.