HandyList allows you to manage a number of lists. As you complete each item you can tick it off, and then delete all the ticked items. Items can be prioritised with colour coding and a list can be exported to a text file.
This app works great on your phone, but is probably unique in that it will also work stand-alone on Android Wear smartwatches - even when the watch is in aeroplane mode or far away from your phone. The "wrist list" mode of the app includes a built-in scrolling keyboard that allows you to enter list and item names directly from your watch! But if you prefer typing on your phone then you can create the list there and send it to your watch instead.
You can also Email or SMS a list to a friend.
The app has been tested on both round (Moto 360) and rectangular (Sony Smartwatch 3) Android Wear watches.