I found this website that has cookie and cake recipes for you:
http://www.eggless.com/
I also found this recipe:
REGGAE BARS
These were originally called "Calypso Bars" (Women's Day Cookie Cookbook), but I've changed it some and have renamed them for 1983! I first made them for Arthur Korb, our jeweler friend who lives in Santa Barbara. He does not eat eggs and loves sweets. I am always challenged to find a cookie recipe without eggs that is really good. This one fits the bill.
2-1/2 squares unsweetened chocolate
2/3 c. hot water
1/2 c. granulated sugar
1-1/3 c. chopped dates
1 c. butter
1 t. vanilla
1/2 c firmly packed light brown sugar
1-1/3 c. sifted flour
1/2 t. baking soda
1 c. chopped nuts
1-1/2 c. rolled oats
1. Melt chocolate in hot water. Add granulated sugar; stir until dissolved. Add dates. Cook over low heat until thickened, about 5 minutes. Blend in 1/4 c. butter. Add vanilla. Cool.
2. Cream together remaining 3/4 c. butter with brown sugar until fluffy. Sift together flour and soda. Add to creamed mixture and blend well. Add nuts and oats and mix until crumbly.
3. Spread batter evenly into a well-greased 10 x 15-inch shallow rimmed baking pan. Sprinkle with nuts, pressing them gently into the batter.
4. Bake in a 325 degrees oven for about 25 minutes or until center feels firm to the touch and the sides begin to pull away from the pan.
5. Cool on rack, then cut into bars.
Makes 30 squares.