Many people think that Turkey is an exotic country probably warm all year round with deserts and camels and everything. Not so!
First, thank God we have no deserts (they are not exactly fun) and the only camels you will see are for tourists only. Second, the country is between latitudes 35° and 43° N and longitudes 25° and 45° E. This means we enjoy all 4 seasons here in this country.
For detailed info you may check out Wikipedia. Another fun fact: There are a few skiing areas within 4 hours of driving distance from Istanbul.
I think the worst times to visit Istanbul are between late October- late March. It is usually pretty cold with lots of rain and some snow. July and August are also terrible choices unless you want to melt your brains.
My favorite time frame is between early April-mid June. In the spring you can see beautiful lavender colored flowers and tulips all over the city and taking a boat trip along the Bosphorus will present you with stunning views. Since it is not so hot and humid yet, it is possible to take long walks and spend lots of time outside. You can make the most of this city if you walk around especially in the historic peninsula.
Mid September- late October is another good option to see Istanbul. The weather is mild and quiet nice during early Fall.
Istanbul gets some snow during the winter but it does not last long as it does in mid Anatolia and eastern Turkey. Since Istanbul is a coastal city, the climate is somewhat milder. However, even a mild precipitation cripples the city traffic beyond comprehension.
So, if you ever want to visit this very historic and cool city, let me know. I can give you some tips as to what not to do. As for what to do, I know you guys do a lot of research before visiting places, so may be you can give me tips about that!