Pulse first 4 ingredients in a food processor until dough leaves sides of bowl. Divide dough into 8 portions, shaping each portion into a ball. Wrap separately in plastic wrap, and chill at least 1 hour.
Remove 1 dough portion, and roll into an 8-inch circle on a lightly floured surface. Spread with 1/4 cup apricot preserves, leaving a 2-inch circle of uncovered dough in center. Sprinkle preserves with 2 tablespoons almonds. Cut circle into 8 wedges, and roll up wedges, starting at a wide end.
Place, point side down, on a lightly greased baking sheet, curving into a crescent shape. Repeat procedure with remaining dough portions, preserves, and almonds.
Combine sugar and cinnamon; sprinkle over each crescent.
Bake at 375° for 15 to 20 minutes or until golden. Transfer to wire racks to cool.
Apple Rugelach: Melt 1/4 cup butter or margarine in a large skillet; add 4 large Granny Smith apples, peeled and finely chopped, and 1 cup sugar. Cook, stirring constantly, 5 to 7 minutes or until mixture is thick and golden. Cool. Substitute for apricot preserves. Substitute 1 cup chopped pecans, toasted, for almonds.