Admittedly, this is more of a green thing than a frugal thing since napkins aren’t terribly expensive. But, they’re not free and so using less of them will save money. Plus, you can feel good about saving some trees by cutting down on your napkin usage(personally, I’d much rather give up napkins than toilet paper!).
A lot of frugal books and blogs that I read suggest using cloth napkins instead of paper napkins. That is certainly a cheap and green alternative, but my preference is to use damp washcloths. My children, dear though they are, tend to get very sticky when they’re eating. Napkins, whether cloth or paper(well, especially paper!), just aren’t very good at taking care of stickiness, but a wet washcloth is perfect for the job.
I use cheap white washcloths that come in a package at places like Target or Walmart. They do eventually wear out, but I’m quite sure that they pay for themselves before they become full of holes. A package only costs a couple of dollars and it doesn’t take long at all to go through a couple of dollars worth of paper napkins.
Washcloths can become stinky pretty fast if they’re not taken care of properly, though. To keep them from smelling bad, I let them dry every night by hanging them on places like the oven door, or over the kitchen sink(leaving them in a wad by the kitchen sink is a very bad idea). Then in the morning, I throw them into the laundry basket, as I don’t ever use the same washcloth two days in a row.
I do line dry most of my laundry, but to kill the bacteria that like to live in washcloths, I use my dryer. I just make a separate pile in my laundry room for kitchen towels and washcloths, and once a week I do a load of those and then throw them in the dryer.
Additionally, every so often I soak the whole bunch in a bucket of bleach and water. This makes them white again and kills any bacteria that have tried to make the washcloths their home.