Does anybody know of an app similar to Palm OS's "Tasks" app?

I have not been able to find any iOS app that comes close to the simple but effective functionality of Palm OS's "Tasks" app (last copyrighted by Access Systems in 2007, I believe). I liked it for the ability to quickly add a new task, prioritize it, categorize it and give it a due date (all possible from your main list screen). But also, and just as importantly, you could make the tasks repeat - and not just on a fixed schedule; you could make the tasks repeat at an interval after completion date.

For instance: an oil change on your car - you normally do that task every three months, right? But what if you get busy and don't manage to do it for five months? Once you check your task completed, you want it to create a new "Change Oil" task 3 months out, not the very next month in accordance with that "fixed" schedule (as most Task/ToDo apps I've seen do). Any old Palm OS users out there will know what I mean. Any Treo or Centro users on this site?

Does anybody know of a similar app for iPhone? "Errands" by Yoctoville comes close, but it doesn't have a desktop component. How I wish Apple would make something like this "native" to their devices, so that you could have an "agenda view" (showing your Calendar events and your ToDo list on one screen) - "Reminders" does not even come close to filling the bill. Microsoft Outlook (Desktop version) is the closest I can think of.