A favorite game at my old elementary school was Tic-Tac-Toe. Like many libraries, mine has a chess/checkers/backgammon(!) table. I thought it would be fun to make a reusable Tic-Tac-Toe game for the kids to play.
You could also play a group game of Tic-Tac-Toe at Storytime! Play everyone versus you or kids versus grownups. Or whatever combination your little heart desires. These would also make a cute gift for a kid (or kid at heart) in your life. I can imagine an adorable little stuffed and sewn version.
To make, cut 4 thick lines out of felt. Cut (at least) 9 rectangles. Mark both sides of them with Xs and Os. I used puffy paint because it's much, much faster, but you could lovingly cut them out of felt or you could print some off in whatever font you want and hot glue them on. I also hot-glued a piece of scrap felt in the bottom right corner to use as storage for the pieces.
Here's a printable version you can laminate. Don't forget to make extra pieces!