This one 'gets it'. I've downloaded and tested a slew of To-Do List apps that run on the iPhone, and they are all good in their own way, so I'd hop from one to the other, never really being able to decide WHICH one was superior to the others. Well, having now just downloaded and tested 'Air Todo', I can finally make a qualifiable decision: THIS one is a keeper that I'll be using from my iPhones main screen.
Be sure to download both the MacOSX and the iOS version of 'Air Todo' and you'll be in To-Do heaven. Although it lacks some key features that make the other To-Do list apps still valuable (for example, the abilities to set up more than one list, or to even reorder items in that list), what puts this one on top of the heap is the ability to synchronize between all of your devices (computers and mobile). Some of the reviews are claiming that it doesn't sync, but that hasn't been my experience. I created a list on my iPhone, and in the time it took me to check the Menu item equivalent on my desktop, the sync had taken place. Similarly, adding an item in the MacOSX version immediately synced it to the iPhone.
Hint: Make sure your settings are allowing synchronization. On both the iPhone and computer versions, be sure the 'Auto Sync' setting is set to "ON". You might also want to set the computer version to "Start At Login". By default, all of those settings are already set to ON. If your iPhone version is not immediately syncing, try dragging down on the entire screen (that refreshes the screen).
Many thanks to the designer, Chongyu Zhu, for an excellent early effort. Add a few more features to 'Air Todo' and my iPhone's 'List Folder' will become less crowded.