Europe (including Turkey) is generally more formal than the United States. As Julie noted, "conservative" is the key -- but the climate also is very warm, so you won't want heavy clothing.
Much of Europe's art is in churches, so you probably will be visiting a church or two on most of your tours. In Istanbul, your tour probably also will incude a mosque.
>> For ladies, a knee-length dress that covers the shoulders would be acceptable almost anywhere, as would a leotard and a wrap skirt. Some churches also require women to cover their heads, so bring a kerchief in your handbag for this purpose if you are not wearing a hat. The mosques seem to provide full-length wrap skirts that you can use to cover your knees during the visit if they deem your dress too short.
>> For gentlemen, a shirt with a collar (golf shirt or polo shirt) and dress slacks are acceptable for sightseeing just about anywhere.
It's best to wear standard (dress style) shoes rather than sneakers.
A few places, like the casino in Monte Carlo, do require dressier attire. Information on dress requirements for such attractions will be readily available either in the tour description or aboard ship.