Which festivals/traditional events are a must-see in Istanbul?

My favorite non-religious holiday is International Children's Day. It was started by Ataturk, the first president of the Turkish Republic. Ataturk was a great advocate for youth education & development, and every year children from all over the world come to share in the festivities. But to be fair, the city is so vibrant any time of year, there's always something exciting to see or do regardless of when you go.

There are quite a few. Depends on what you like really.

If you go there between late August-mid May definitely consider catching a futbol (a.k.a soccer) game either in Turk Telekom Arena (home of Galatasaray club), or Sukru Saracoglu Stadium (home of Fenerbahce club) or Inonu Stadium (home of Besiktas club). If you stay close to historic peninsula I think Inonu Stadium is the closest. Sukru Saracoglu is on the Asian side. You may need a ferry ride. Turk Telekom Arena is also in the European side like Inonu but it's a bit far. However, you can catch subway to get there. It's brand new and roads around the stadium are not yet finished. Fans are crazy but I guarantee you it's hard to match the passion of these fans, especially if you are from the U.S. (closest concept in the U.S. is college sports fans but it's not even close). So definitely try to see a futbol game there if you have time.