Map My Walk, Runkeeper and The Moves are all excellent apps for tracking daily walking distances. They each use your smartphone and GPS to track how far you walk.
Map My Walk is available for Android and Apple phones. It uses the phone's GPS to track the distance you travel each day, as well as providing a calendar of where you walked. The newest feature of this app is the ability to add custom challenges.
Runkeeper is meant for runners, though you can also use it to track your walking distances and speeds. It also helps to chart the person's weight loss or training. The Moves is for iOS on Apple phones only. It is a basic app that uses a colored circle to count daily steps.