Cheesecake is one of those desserts that can have a few pitfalls, but if you follow these simple tips, your cheesecakes should turn out just fine. Note that these cheesecake tips don't necessarily appear in order of importance. Rather, I've tried to order them roughly in order of the actual steps of baking the cheesecake.
Also see: New York Cheesecake Recipe
To start with, I probably don't need to mention this, but I will anyway: Don't use cream cheese that came from one of those plastic tubs. Only use those rectangular blocks of cream cheese. The stuff in tubs has air whipped into it and it won't work out the same way. Also, full-fat cream cheese (and sour cream) works best.
Room Temperature: Make sure all ingredients — the cream cheese, sour cream, eggs and even the sugar — are at room temperature. This will allow the ingredients to blend together better, giving you a smoother cheesecake.
Don't Overbeat: Overbeating can cause the cheesecake to crack when you bake it. So, when you're combining the sugar, cream cheese, eggs and other ingredients, do it on a medium-low speed. The paddle attachment (as opposed to the whip attachment) of a stand mixer is best so that you don't beat too much air into the batter.
Use a Springform Pan: The best pan for baking a cheesecake is a springform pan. Make sure the bottom is greased when you press the graham cracker crumbs into the bottom, and also make sure the sides of the pan are well-greased when you pour in the batter. Melted butter is great for greasing the pan, but you can just rub it with butter or even spray it with cooking spray. They make springform pans with a nonstick coating, but grease it anyway.
Keep it Moist: A dry cheesecake will also crack. To prevent this, we bake a cheesecake with a pan of water in the oven. A steamy oven will prevent the cheesecake from drying out. Note that this is similar to the way we bake a creme brulee in a water bath — both creme brulee and cheesecake are essentially baked custards. But when we bake a cheesecake, we don't put the springform pan in the water, because it might leak. Just put the roasting pan of water on the lower rack and bake the cheesecake on the upper rack.
No Peeking: Don't open the oven while baking! You don't want to let all that steamy air out. Also, changes in temperature during baking can cause the cheesecake to crack or sink in the middle.
Also, No Poking: Don't poke anything into the center of a cheesecake to see if it's done. You'll just make a hole in it. That goes for instant-read thermometers. It so happens that when the center of a cheesecake hits 150°F, it's done. But the only way to know that is to poke it with a thermometer. Don't do it. Instead, just give it a jiggle. If it's firm at the edges and still wobbles a little in the center, it's done.