The bosphorus cruise is something of a tourist institution. It is also (during the high season) considered to be a bit hellish. Basically, it's on very similar boats as the ferries, but because it's aimed at foreigners and has an extra long journey, it is 25tl round trip instead of the 4tl it would take for a ferry round trip. They are offered at eminonu, Kabitas, and Besiktas and go up to the black sea, make a few stops, and come back. A few of my friends have really enjoyed the trip, but the boat is going to be packed full of tourists and children and the like from may until october, which makes it a bit crazy. If you go, make sure you go with the IDO run one and not the private companies, and try to leave early in the AM.
A better alternative is (I think) using non-tourist oriented public transport to get to the black sea. You can take a bus up the coast to Sariyer and then take a ferry from there to Anadolu Kavagi, the old castle on the asian side overlooking the Black sea. It's a really scenic area and doesn't get too packed, even in the heat of the summer. On the way home, traffic will be pretty bad, which is a good excuse to stop in Bebek or Arnavutkoy (Go to Bodrum Manti for excellent turkish Ravioli) for dinner, ice cream, and beer.
Or, if you are really set on a boat ride, the ferries out to the prince's islands are awesome, and as long as you don't get off at Buyukada, (the last stop) the islands are relatively calm and much less crowded.