The show will carry on and will always be his legacy. There are many people behind the show, many talented writers, Conan was one of them as well so the show will surely remain as long as there are people with ideas for it :)
When the series finished or Matt die, I hope they have a special farewell episode for all fans. In this episode, we fãs might remember the best moments spent with family and with the series. Better yet, SURPRISE US, as you have done over the years. Soo important, my little guys :D Hope you never run out!