Thanks to Suzanne Long for this Frugal Baby Tip!
When my first was born, almost 18 years ago (sniff!) I started always carrying a wet wash cloth in a ziplock bag with us when we went out to wipe her hands, face, whatever.
As we have had more kids, I have continued this routine,packing one wet wash cloth per child, even the ones who weren't in diapers. They have come in handy so many times over the years. I currently have a 16 month old in cloth and his baby brother is due in about 10 weeks.
When changing a messy diaper when out, I just use one of the wash cloths to wipe him and stick it in the bag with the wet/soiled diapers - it then just gets washed with the diapers. I have tried using smaller cloth wipes at home, but have found that I now pretty much use the wash cloths for wipes, even at home.
You can get a pack of 18 adult size wash cloths at Walmart for a little under $4.