Here's a fun little project I made about a year ago. We use these scripture puppets to help my daughter learn the stories from the Bible and Book of Mormon. I made the basic characters--a king, a prophet, an angel, etc. and we use them over and over. Sometimes I even make "props" to go along with specific stories---cardboard trees, cotton ball sheep, etc. She LOVES them and gets so excited to act out the stories.
They were really simple to make: I just traced the basic shape onto two pieces of craft felt and sewed them together along the outside edges. (Make sure they are big enough that dad can fit his hands in the holes too.) Then I used skin-colored felt to make the heads and decorated them with little embellishments I had lying around. The puppets have googley eyes, but just a warning---all kids I've ever met like to pick googley eyes off of things. GRR!! I'd never add googley eyes to anything I make ever again if I didn't think they were so stinkin' cute!
Anyway, the sky is the limit with this project. You could make all sorts of characters from the scriptures, or you could go a different direction and make animal puppets, storybook characters, puppets that look like each member of your family...so many fun options!