I have an old Betty Crocker dessert cookbook where I take recipes from. Although I don't do cookie exchanges, I'll make some of these for Christmas parties and they usually go over well:
http://www.bettycrocker.com/recipes/almond-thumbprint-cookies/74f34f8d-9266-4662-b3f8-7ba34dc7d357
Thumbprint cookies (I use raspberry and mint jelly for red & green, but will sometimes put a few grape jelly ones because I think that's the best flavor) similar to the above recipe, but I use walnuts instead of almonds and jelly instead of the curd.
Butterballs, aka Russian Teacakes, aka Mexican Teacakes (and several other names) are always popular. For the holidays, after I roll in the powdered sugar, I'll put a light sprinkle of red or green colored sugar just to give them a little holiday color. There are tons of recipes on-line for these.
I also make the peanut butter kisses like this recipe, but using Hershey's kisses instead of chocolate stars:
http://www.bettycrocker.com/recipes/peanut-butter-chocolate-cookies/f85b72ed-8a53-4a9a-8897-f0befe46a55f
I've made Nestle tollhouse cookies using red & green M&Ms pushed into the tops.