Plastic grocery bags--if you’ve got a couple without any rips or holes in them, since they must be waterproof--may help keep your feet dry when you encounter soggy patches in your favorite hiking trail. Test each plastic grocery bag for waterproofness before you reuse it. Fill the bag full of water: If the water leaks out, obviously water will be able to leak in on the trail, too. Once you’ve found a couple that hold liquid without leaks, fold them down (they pack to almost nothing) and stow them in the bottom of your pack until needed.
Once the going gets soggy, just pull off your shoes or boots, slip each foot into a fully intact plastic bag, and put your shoes back on. Yes, your shoes will get muddy; there’s not much you can do about that. However, inside the plastic bags your feet and socks stay nice and dry. Take the bags off as soon as possible to keep condensation from building up inside the bags.
Trying to make a style statement on the trail? Trim away the bags where they stick out from the top of your shoes or boots, and nobody will ever know you have them on. They'll just marvel at how you can tromp through the muddiest of patches with nary a worry about getting cold, soggy feet.