Todo.txt is one of the most basic todo lists that can be found. It is much like a text editor, except it syncs across devices.
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Pro Easily editable format
Todo.txt can be edited in plain text and then displayed with neat styles.
Pro Command line support
You can edit your lists using the command line (e.g., Terminal) via a supplied bash script.
Pro Full control over your to-dos
You have full access to the underlying programming rules, and therefore total control over your task lists.
Pro Works with lots of apps for every platform
Todo.txt lists can be edited in virtually every text editor ever made and accessed on devices that support Dropbox. The user community has also created a number of apps for dozens of platforms.
Pro Editable from any text editor without needing any proprietary software
Because todo.txt is just a todo standard with various compatible apps to edit it, you can update it from any device as long as it can edit text and you can access your todo.txt file
It's convenient to be able to access your todo list quickly via your programming environment so you don't have to switch contexts, and to have a separate todo.txt file per project.
Pro It's free
It runs on MacOS, Android, and Python (in the Mac's Unix CLI) -- all for free.
Pro Wide range of interface apps
The community has developed a wide range of apps that interface with the basic file structure. These apps vary in how much they accomplish, how much hand-holding they do, their level of glitz, etc. They range from plugins for an editing app like vim to stand-alone, platform-specific GUI's. So YMMV depending on what you use. (todopy is particularly nice, a Python program that has a "console" mode which provides a keyboard-driven GUI.)
Pro It's easily extensible, and in fact has been extended to include most things people want
Pro Easy syncing
Todo.txt automatically and seamlessly syncs through Dropbox.
Pro Easy to sync up between lots of devices and interfaces
At a bare minimum you just need to be able to edit text, but there are many apps and advanced interfaces you can install on many devices to supplement your to-do list editing.
Con No support for reoccurring tasks
Tasks have dates corresponding to creation and completion, but there is no explicit support for due dates or for tasks that reoccur.
Con Nested tasks not supported
Many todo tasks for developers end up having sub tasks that need to be performed for a parent task to be completed, but the todo.txt format does not have any nesting.
Con Android app not updated since 2013
The app only seems to support Dropbox. It would be nice to see support for different and newer file storage services.