This is a task / todo list written in PHP. It requires no SQL database whatsover, all the data is saved in a JSON text file.
The visual side is made with excellent HTML5 Kickstart framework.
Why use this over something like remember the milk, wunderlist or any other cloud service?
Nobody selling your data
Nobody monitoring your activity
Data is easy to get out (no vendor lock-in) and to backup.
Offline mode? Host it on your local machine with a LAMP/WAMP/MAMP server.
Sync? Use a syncing service on the hosts (owncloud and sparkleshare are quite good) and point the program to a json file in that folder.
Offline sync? Combine above 2 points, or put the software in a git, svn or other version control system repo.