Position one rack in center of oven and second rack in lowest third of oven; preheat oven to 350°.
Mix cracker crumbs, 1/4 cup sugar, and butter in a small bowl until well blended.
Press mixture into bottom of 9-inch springform pan with 2 3/4-inch high sides.
Using an electric mixer, beat cream cheese and remaining 1 cup sugar in large bowl until smooth.
Add eggs 1 at a time, beating just to blend after each addition.
Mix in vanilla.
Fold in sour cream thoroughly.
Pour batter into prepared pan.
Set cheesecake pan on center rack.
Fill small pan with water and place on bottom rack.
Bake cheesecake for 30 minutes.
Turn off heat and let stand in warm oven for 1 hour. Do not open oven door.
Transfer to rack and cool.
Cover and chill until cold. (Can be prepared 1 day ahead.)