The sequential nature of the creation story makes it perfect for many kindergarten activities. Draw pictures of the objects created each day on various cards (e.g., one card containing the sun, moon and stars), and then have kindergartners put them into the correct sequence. You can make crafts with them for each day of the creation story - a black and white picture for day one, an animal craft for day six and a pillow for day seven. To help them understand how man was created, make gingerbread men and explain how all people were made from the same material.
Noah's Ark is probably the most popular Bible story among this age group. Reinforce the story by playing a matching game in which children find pairs of the animals that were on the ark, but really any animal-related game or activity would work well. Alternatively, build your own ark dioramas out of shoe boxes. Help kids divide the ark into three levels and put crumpled paper (garbage) on the bottom level, cut-out pictures of animals on the middle level and paper dolls (people) on the top level.
The Exodus of the Jews from Egypt can seem extremely exciting for young children, especially the climax at the Red Sea. Bake each child a small cake and let them cut it in half, leaving a space between the two halves as the section that the Jews walked through. They can then smear blue icing all over the cake and add tiny jelly beans as the people walking through the sea. Alternatively, they could decorate a paper towel roll as Moses's staff.
Any Bible story lends itself to basic activities. Kindergartners often enjoy acting out the story, either with their own bodies or with puppets. Give them different colors of playdough so they can make the scenes in still life. If children are familiar with various Bible stories, encourage them to play a guessing game in which one child describes a Biblical character and the others have to the identity of the character.