Preheat oven to 350°F (175°C). In a medium bowl, combine graham cracker crumbs, sugar, and melted butter. Press the mixture firmly into the bottom of a 9-inch springform pan.

In a large bowl, beat the softened cream cheese and sugar together until smooth and creamy. Beat in the eggs one at a time, mixing well after each addition. Stir in the sour cream and vanilla extract until just combined.

Pour the cream cheese mixture over the crust in the springform pan. Place the springform pan in a larger roasting pan. Fill the roasting pan with hot water halfway up the sides of the springform pan.

Bake for 60-75 minutes, or until the edges are set and the center jiggles slightly. Turn off the oven and leave the cheesecake inside with the door ajar for 1 hour.

Remove the cheesecake from the oven and water bath. Let it cool completely on a wire rack, then refrigerate for at least 4 hours, or preferably overnight, before serving.