The fourth day of Christmas is usually associated with children, especially orphaned or abandoned children. Not having any children myself, I really didn't know what to write about this day but I think that a good tradition would be just to spend a little extra quality time with your kids today, no gifts included. Perhaps spend the day doing something they get to choose, like going to the zoo or another favorite place. Maybe just build a fire in the backyard and roast marshmallows. If your kids are grown, take them out to lunch or write a letter telling how proud you are of them.
There are also many charities founded for the benefit of abandoned or terminally ill children, so if you have the means and no children, perhaps a donation there. St. Judes is a wonderful and longtime organization that does wonderful work for kids.
I think it is also a good idea for parents to get their children to gather up the toys and clothes they no can longer use and involve them in donating the items for needy kids. This way the kids can see, at an early age, that there are many out there less fortunate and hopefully will help them grow into grateful adults. From what I see, most kids really get into stuff like that and are happy to do it.