I know lots of people reuse plastic ziploc bags. I’ve done the washing-drying-reusing thing myself many times to save money and the environment. Turns out it is an unsafe practice. You can’t get it sterilized well enough to kill the bacteria. No matter how hot your water is there are still little crevices that you can’t get into. So you should NOT reuse them.
There are other ways to store your foods instead of plastic baggies though. I limit them to food being carried to a location where the container won’t be returned, trips to the zoo, field trips, etc. My kids take their lunches everyday so we like to use containers. Rubbermaid makes some great ones and Ziploc has been a staple in our household. My oldest son seems to be having a problem with his friends using his sandwich boxes to crush things (it eventually breaks the boxes. Oh! and his thermos! Any suggestions?
Please remember that plastic bags are recyclable if you do decide to use them. Just keep in mind that they need to be pretty clean and dry. I know our Walmart has boxes in the front of the store for recycling.