I like the simple and straightforward interface of the Reminders.app: edit reminders inline, and add a reminder by tapping and typing in the next empty line. So I wrote a UITableViewController subclass that does just that, but adds Edit mode with reordering.

Coding reordering requires implementing methods from both of the two entangled protocols UITableViewDataSource and UITableViewDelegate.

In UITableViewDataSource we have the methods:
tableView:commitEditingStyle:forRowAtIndexPath: (for insert and delete)
tableView:canMoveRowAtIndexPath: (for reorder)
tableView:moveRowAtIndexPath:toIndexPath: (for reorder)

And in UITableViewDelegate:
tableView:editingStyleForRowAtIndexPath: (for insert and delete)
tableView:targetIndexPathForMoveFromRowAtIndexPath:toProposedIndexPath: (for reorder)

The UITableViewDelegate methods are not strictly necessary in the simplest case where all rows are deletable, no row is insertable, and all rows are reorderable. In fact, in this simplest case you don’t need canMoveRowAtIndexPath either, only this:

- (void)tableView:(UITableView *)tableView
    moveRowAtIndexPath:(NSIndexPath *)fromIndexPath
    toIndexPath:(NSIndexPath *)toIndexPath
{
    // Update the model with the change.
    // The view updates are already handled by UIKit.
}

But of course, if the last row (or the row past last) is an insert row, and is not reorderable, than you need to implement the other methods as well. You can get the code for that (along with the inline editable UITextField-s) at GitHub: http://github.com/yonat/EditableList.