Haven't seen this mentioned anywhere and I've been using it for the last few weeks, and love it. It you're after an all singing, all dancing to do list app which syncs with your computer then this is NOT the app for you. However if you want one where it's easy to see the important things, such as tasks to do, task completed then carry on reading.
It's called
Put Things Off and it is a very simple to do list app. It costs £1.79 and you basically create a task, then have the option of setting a date. When that day comes around it appears in your "today" task box (and a red badge appears on the app icon on the home screen), you can then see what tasks you have that day. If you complete it, you hit the star icon on the task and it goes to your completed tray, if you don't, you press an arrow icon, and it gets put off for another day (you choose the length of time it's put off for) and so the cycle continues.
Very simple, very effective, and the best to-do list app I've found so far.
Quick trailer video here:
YouTube - Put Things Off for iPhone
Official site
here with a proper demonstration video