Plancake is free, open source software under the AGPL license.
Task Management Organize all your projects and all the things you need to do in one place with the help of an Inbox, intuitive item reordering, lists, tags, repeating tasks, keyboard shortcuts, a calendar and a very easy-to-use interface.
You will feel you have everything under control.
GTD (Getting Things Done)tm If you want, you will be able to implement the well-known GTD methodology in order to achieve stress-free productivity.
Dump what is on your mind to your Inbox, filter lists by tags (contexts) and light up cute stars to flag up next actions.
Notebook All your ideas and notes will always be at hand, wherever you are.
You will get a Word-like editor where you can add even images.
There's also an API and mobile apps/sync.