I usually do spritz cookies, chocolate crinkles, stained glass cookies (which are time intensive, as you have to not only cut out dough and the holes in the cookies, but fill them with crushed Jolly Rancher candies. We found Jolly Rancher works MUCH better than Lifesavers) ice box cookies, a cookie where we hide candies, or nuts (and label them for people with allergies) or dried fruit inside, we also sometimes do these labor intensive cookies where you make a stiff dough, dye it different colors and then use it like clay to make fruits and vegetables out of the cookie dough.
Most of our recipes are in the totally retro, totally cool Betty Crocker's Cooky Book
There's an interesting cookie called a "Colorful Cookie" and you make it with flour, sugar and Jello. There are no eggs in it, and it is really easy to make.
1 pkg (3 ounces) fruit-flavored gelatin
1 cup powdered sugar
1 cup margarine or butter softened
2 and 1/4 cups plain flour (or a little less if you like the cookies less crispy)
1/4 tsp salt
preheat oven to 350 degrees. Reserve 1 tbsp dry gelatin for the glaze. Mix remaining gelatin, powdered sugar and margarine. Stir in flour and salt. Shape dough into 1-in balls. Place about 2 inches apart on ungreased cookie sheet. Bake until set but not brown (8 to 10 minutes) cool slightly. remove from cookie sheet. Cool.
I like to a number of boxes of Jello and make different colors. I also sprinkle sanding sugar on top to complement the color of the cookie.