Perhaps the most important of the distinguishing factors of the App Store and iOS development is the insanely high quality of apps. Not all apps -- not by a long shot -- but the ones that are made with care and attention are truly wonders of form and function wrapped in a gorgeous shell. Due is one of those apps. It takes the mundane task of setting a quick reminder and makes it easier than using a calendar app and more, dare I say it, fun than it should be. No tricks, just good solid design and all the functions you need within easy reach.
Make no mistake, Due is just a to-do list with timers, so if you're looking for something else, Due isn't for you. But if you ever used Diddlebug on the ancient Palm OS, this is as close as I've found (with Diddlebug you drew on the screen and added a timer). Why there's no iOS version of Diddlebug is beyond me, even a crappy 8-bit version would suffice. At any rate, Due allows you to create a timed reminder with a default notification and chime within about 4 or 5 taps, depending on some options. Four if you accept the default timed "on the next quarter hour." You can adjust the default time interval in the app's settings, from 1 minute to 30.
Reminders, once created, go in a queue. Tapping on a reminder allows you to set whether or not snoozing is allowed, if you want a reminder to repeat, chime options and if you want to reschedule this for 10 minutes, 1 hour or 1 day later. All of that in a submenu, and it's quite intuitive to boot. Swiping a reminder allows you to delete it.
An example of the app's lovely attention to detail: when you go to set a reminder, there are four "default time" buttons which correspond to when you wake up, what time you eat lunch, when you leave work and just before bedtime.