Oil tankers do indeed dominate the issue today. When Montreux was signed in 1936, a 10,000-tonne tanker serving the Black Sea ports was big, and the shores of the Bosphorus itself were green. Today Istanbul has grown from around half a million inhabitants to some 15-mil citizens, its suburbs lining both sides of the twisting waterway, and tankers that may be more than 250 meters long have to navigate tight bends, one of which is located where the strait is less than 700 meters wide...
Map of the Bosphorus:
Results of a collision in the transit lanes:
(Bosphorus map and photo from here)
When I was much younger and lived in Turkey, I transited the Bosphorus on a liner, by ferry and visited some islands in the middle of it. One of my friends lived in a house right along it. What I learned from all that was that it is a narrow, heavily trafficked sea lane. I can well understand the encouragement of pipelines to replace the tankers plying the strait. And the concerns over terrorism.
Update: Another source of info in this choke point is from the US Department of Energy which has this great photo of the strait:
Under the Montreux Convention of 1936, commercial shipping has the right of free passage through the Bosporus and Turkish Straits in peacetime, although Turkey claims the right to impose regulations for safety and environmental purposes.
Earlier information on other sea lanes here and here.