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

Prepare the Filling

In a large mixing bowl, beat the softened cream cheese until smooth. Gradually add the granulated sugar and beat until well combined. Add the sour cream and vanilla extract, mixing until smooth. Add the eggs one at a time, mixing well after each addition.

Add Flavor Variations

Divide the filling into portions if making different flavors. Add fruit puree, chocolate chips, lemon zest, or almond extract to each portion as desired, mixing gently to incorporate.

Bake the Cheesecake

Pour the filling over the crust in the springform pan. Bake in the preheated oven for 50-60 minutes, or until the center is set but still slightly jiggly. Turn off the oven and let the cheesecake cool in the oven with the door ajar for 1 hour.

Chill and Serve

Remove the cheesecake from the oven and let it cool to room temperature. Refrigerate for at least 4 hours, preferably overnight. Release the cheesecake from the springform pan, slice, and serve with toppings of your choice.