There is already a question on reordering of items in the reminder app, but I want to go one step further and move existing items from the device to iCloud. Is that possible at all?
You can't seem to drag lists down to iCloud, nor can you seem to drag an item(s) from one list to another - but you can move items using the context menu
Create duplicate lists in the iCloud section of the list of lists...(you can probably see one called 'reminders' there already)
Go back to the list you want to move highlight all items in the list (not the text in one item but the item itself) - then bring up the context menu and select move... chose your duplicated list as destination
You may also wan to move the completed items from the old list itself to the new click on the 'completed' at the top of the list
Go to Settings > iCloud (Alternatively, Settings > Mail, Contacts, Calendars > iCloud) and make sure Reminders syncing is on.