Well, here are a few. I hope they are suitably out of the ordinary!
When my cousins and I were little we had a toy train. It lit up, had smoke come out of it, and made noise. We would sit around the track on Christmas Eve and pass notes around.
When we go to church my one cousin (Gabrielle) and I always take the programs they give you and a pen or two and write/draw things for each other. We also have taken to donating to the church when we have money on that day, or if we don't have money, amusing ourselves by writing/drawing on the slips and taking them home with us.
My very favorite that started relatively recently is the Hobo Christmas Tree. It was always my Grandmother's job to set up and decorate the Christmas tree, so when she passed away my Grandfather didn't want to set one up. My cousins and I weren't going to have it. We asked if we could try to set something up and got permission.
We immediately started rummaging upstairs, where all the decorations were. We got what we could and went into the living room. We took a chair from the kitchen and covered it in a Christmas blanket, putting a tree skirt under it and a light-up Santa Claus on the tree skirt. We wrapped garland around it and tried a set of lights. They didn't work. I sent my cousin back upstairs while I worked on trying to get something to lie right (forget what it was, it took effort though).
We patiently wrapped the lights around our "tree" and then crossed our fingers and plugged everything in. IT WORKED! We were so happy.
There are probably one or two things I'm forgetting about it but that's the gist of it. Now we set one up every year