Pocket Lists

Try shaking your iPhone when inside a list, or at the list of to-do lists — all to-dos will be rearranged.

Integration can be enabled via syncing with the Reminders app.

Pocket Lists Free: http://itunes.apple.com/us/app/pocket-lists-free-checklist/id550086695?mt=8

When inside a list, or when viewing a list of to-do lists, just pull down the entire list, and then release. All syncs will be updated.

To-dos are not deleted when you complete them.
If you are working with to-do stream, then completed to-dos are just not being shown.
And if you are inside a list, then completed to-dos stay where you have completed them.

If you want to continue working with the to-do stream, and have access to your to-dos, connect your stream to a to-do list. In the app go to Settings > Stream > Inbox List. This will put all to-dos added directly into the stream, into selected to-do list.
This will not change to-do stream behavior, but will allow to access completed to-dos in the future — they will always remain in the selected inbox list.

Currentl Pocket Lists is available in English and Russian. More languages are planned, though for now we do not disclose the ETA.

I don't think we will integrate the ability to temporary move to-dos between lists. For now only a permanent move is available (when inside a list, enable edit/sorting mode by tapping a three-striped icon).
For temporary to-do display you can temporary prioritize to-dos (increase their priority), which will make your to-dos be displayed in the Stream.

Please use hierarchy feature for this purpose.

In the iPhone/iPad app, go to Settings > Pocket Lists Cloud > Account to update your profile information and password.

On the main “Lists” screen pull down the entire list of to-do lists. The search form is there.

Due date can be converted to a due time automatically only when there is an active sync with the Reminders app. Unfortunately, Reminders app does not allow adding to-dos with due dates — only exact due time to-dos are allowed (you may try it yourself in the stock Apple's Reminders app).

When Pocket Lists is trying to send Reminders a to-do with due date, Reminders automatically converts it into this date's 00:00 time. That's confusing, so instead of 0:00 we made it such that 10:00 is sent automatically to the Reminders app instead of an all-day. That 10:00 time is configurable in the Pocket Lists's “Settings > Due Notifications” screen.