Indoor Games
Games can be just as fun inside as they are outdoors! You could play board games, card games, even charades. Teach them one of your favorite childhood games and take a walk down memory lane. The kids could even make up their own games; help them write down the rules so they can teach their parents and friends how to play.
Arts and Crafts
Arts and crafts keep kids busy while letting them express their creative nature. Tear a few sheets from a coloring book, grab a 64-pack of crayons and settle the kids down at the table for some coloring. You could even do some finger painting -- just make sure to cover your workspace and put smocks on the kids in case it gets messy.
Cooking
Instead of the kids just eating their snacks, why can't they help make them too? Some kid-friendly recipes are "ants on a log" (peanut butter-filled celery sticks with raisins on top) and Rice Krispy treats. Just make sure it's okay with parents for you to use the kitchen, check on any food allergies, and be careful if you use the stove!
Reading and Writing
Reading is a classic rainy day activity. Bring some classic kids' books over -- Shel Silverstein and Dr. Seuss books always make good choices. If the kids are old enough, do "popcorn reading": each person reads a paragraph, passing the book around until the story is over. For younger kids, have them make up their own stories and draw pictures to illustrate what happens.