Recently I found a simple but very convenient TODO-shnik script on the network, the script works on php + ajax both with MySQL and without it.

The current version at the moment - myTinyTodo v1.3.2
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OpportunitiesMultiple list support
Task Notes
Tags, tag cloud.
Deadline for the task
Task Priorities (-1, 0, +1, +2)
Sort tasks by dragging, by priority, by date of execution
Search
Password protection
Smart syntax to quickly add a task (example: / + 1 / Task / Tags /)
Customized styles for print and mobile
Demo -
http://www.mytinytodo.net/demo/Read more on the author's website -
www.mytinytodo.net/