I've searched around and haven't found an app that is for setting reminders. I know you can just set something in the calendar, but I don't want a simple reminder staying in the calendar.

I would like to see an app that you can load up, set a reminder, set a time to remind you if you would like, maybe set a repetition, and have it remind you with a popup on the lock screen and/or homescreen. Then, once you mark the reminder completed, it deletes from the database.

I have such a horrible memory that it would be nice to just quickly load up an app, type a reminder (e.g. don't forget to bring book), tell it to remind me at 6am, and be on my way. This app could include a todo list, notes, etc. I've seen webapps llke this, but I would like a native app because I don't always have access to the internet.