Cheesecake is basicaly a cheese custard in a graham cracker crust. As the custard temperature rises above 165' or so, the protien in the egg sets and contracts. As with all things, when it cools, it also shrinks. It is this shrinking of the cheesecake that causes the cracking. The crust is immovable, and hold tight to the custard where it meets. As the custard cools, it tries to shrink, but can't shrink in diameter, especially on the surface. The surface is too dry, and isn't elastic, and so it cracks accross the center.
As was said by several, cooking until the custard is set, but still jiggles a little will give the custard suffiecient elasticity to not crack as the custard cools and shrinks. Plus, it won't try to shrink due to the egg setting.
The goal is to create a custard that is creamy, yet with enough body to hold its shape when sliced.
Sometimes I want a more dry, dense, and heavy cheesecake (overcooked texture), topped with sweetened sour cream or a fruity pie filling such as blueberry, cherry, or apple. When the cheesecake is topped, the crack is hidden and makes no difference. When I want a creamier cheesecake, cracking just isn't a problem. I don't use a water bath with either, and the cheesecake comes out great.
Final temperature is the deciding factor of both the texture of the custard, and whether it cracks or not.
The idea of cooling the cheesecake with the oven, is that the cheesecake will cool more slowly, creating less stress that can create the dreaded crack. I have found that it really doesn't help if the cheesecake has been overcooked. But it still tastes great.
Also, be aware that there are many variations to cheesecake, some made with cream cheese, others made with cottage cheese, ricotta, or Neufchatel. Some incorporate orange rind in the recipe, while others don't. There are both savory and sweet cheescakes, some made with ladyfinger crusts, or crushed Oreo cookies, or the more familiar graham cracker crust.
Don't be afraid to try different kinds of cheesecake. They are all wonderful. My personal favorite is a New York cheesecake with a sweetened sour cream topping. But the Holywood cheesecake is an amazing thing as well.
Have fun and experiment. I've even taken my New York cheesecake recipe and added cream to the original ingredients, and come out with a super rich and creamy version. It's all good.
Seeeeeeeya; Chief Longwind of the North