This easy technique makes lick-and-stick paper for envelopes, stamps and stickers. It's cheap, fast and easy, but takes a little planning ahead because the glue needs to dry before use.
Take four packets of unflavored gelatin and dissolve it in about a a third of a cup of hot (close to boiling) white vinegar. You can also add up to a tablespoon of vanilla extract or other flavoring, although with very small children this might encourage them to eat the paper. Stir well. While the mixture is still hot, use a sterilized paintbrush or toothbrush to paint it on the back of the paper you wish to use. Work fairly quickly, because the mix will begin to gel up as it cools. Hang and allow to dry.
Another recipe involves mixing equal parts vinegar and white glue, and applying as above. I've never tried this since I'm a little uncomfortable asking the kids to lick something that has a non-food ingredient. (And I probably have seen one too many episodes of Seinfeld.) Of course, they could always wet it with sponges instead.
Once the papers have dried, you simply lick or otherwise moisten the painted side to make it stick to other papers. A fun project stemming from this recipe would be to have the kids create postage stamps. They can make small designs on the paper and then cut them out with stamp-edged specialty scissors (about $2 at the craft store). You can put on the glue either before or after they make their designs. Stick them to envelopes and have them send messages to their friends!