For a year now my family has been using these compact micro fiber beach towels by Acteon. They take up a fraction of the space that a regular towel does and they work really well in a pinch. All 4 of them take up less space than a traditional terry cloth towel. You can throw all of them in a small bag and take to the beach or pool.
We use these towels when we go camping, and on trips where we know we'll need towels with us. We purchased the 4 pack so that each one of us could have our own.
In addition, we use one of their gym towels which are great for working out (we use with our Peleton Bike). You can get the gym towel direct from their website.